COLLEGE  OF  AGRICULTURE 
DAVIS,  CALIFORNIA 


OUTLINES  OF  PHYSICAL  CHEMISTRY 


OUTLINES  OF 

PHYSICAL  CHEMISTRY 


BY 


G.   SENTER,   D.Sc.  (LOND.),   PH.D.  (LEIPZIG) 

LECTURER  ON   CHEMISTRY  AT  ST.  MARY'S   HOSPITAL,  UNIVERSITY  OP  LONDON 

LECTURER  ON  PHYSICAL  CHEMISTRY,  CASS  TECHNICAL  INSTITUTE,  ALDGATEJ 

FORMERLY  EXAMINER  IN  CHEMISTRY  TO  THE  ROYAL  COLLEGE  OP 

PHYSICIANS  OF  LONDON  AND  THE  ROYAL  COLLEGE  OF 

SURGEONS  OF  ENGLAND 


UNIVERSITY  OF  CALIFORNIA 

LIBRARY 

COLLEGE  OF  AGRICULTURE 
DAVIS 

THIRD    EDITION    REVISED 


Chas  S.Bisson. 

NEW    YORK 
D.    VAN   NOSTRAND    COMPANY 

23  MURRAY  AND  27  WARREN  STS. 

1913 


PREFACE  TO  FIRST  EDITION 

THE  present  book  is  intended  as  an  elementary  in- 
troduction to  Physical  Chemistry.  It  is  assumed 
that  the  student  taking  up  the  study  of  this  subject  has 
already  an  elementary  knowledge  of  chemistry  and  phy- 
sics, and  comparatively  little  space  is  devoted  to  those 
parts  of  the  subject  with  which  the  student  is  presumed 
to  be  familiar  from  his  earlier  work. 

Physical  chemistry  is  now  such  an  extensive  subject 
that  it  is  impossible  even  to  touch  on  all  its  important 
applications  within  the  limits  of  a  small  text-book.  I 
have  therefore  preferred  to  deal  in  considerable  detail 
with  those  branches  of  the  subject  which  usually  present 
most  difficulty  to  beginners,  such  as  the  modern  theory 
of  solutions,  the  principles  of  chemical  equilibrium,  elec- 
trical conductivity  and  electromotive  force,  and  have 
devoted  relatively  less  space  to  the  relationships  between 
physical  properties  and  chemical  composition.  The  prin- 
ciples employed  in  the  investigation  of  physical  proper- 
ties from  the  point  of  view  of  chemical  composition  are 
illustrated  by  a  few  typical  examples,  so  that  the  student 
should  have  little  difficulty  in  understanding  the  special 
works  on  these  subjects.  Electrochemistry  is  dealt  with 


iv          OUTLINES  OF  PHYSICAL  CHEMISTRY 

rather  more  fully  than  has  hitherto  been  usual  in  ele- 
mentary works  on  Physical  Chemistry,  and  the  book  is 
therefore  well  suited  for  electrical  engineers. 

From  my  experience  as  a  student  and  as  a  teacher,  I 
am  convinced  that  one  of  the  best  methods  of  familiarising 
the  student  with  the  principles  of  a  subject  is  by  means 
of  numerical  examples.  For  this  reason  I  have,  as  far  as 
possible,  given  numerical  illustrations  of  those  laws  and 
formulae  which  are  likely  to  present  difficulty  to  the  be- 
ginner. This  is  particularly  important  with  regard  to  cer- 
tain formulae — more  particularly  those  in  the  chapter  on 
Electromotive  Force — which  cannot  easily  be  proved  by 
simple  methods,  but  which  even  the  elementary  student 
must  make  use  of.  The  really  important  thing  in  this 
connection  is  not  that  the  student  should  be  able  to  prove 
the  formula,  but  that  he  should  thoroughly  understand 
its  meaning  and  applications. 

I  have  throughout  the  book  used  only  the  most  ele- 
mentary mathematics.  In  order  to  make  use  of  some  of 
the  formulae,  particularly  those  in  the  chapters  on  Velo- 
city of  Reaction  and  Electromotive  Force,  an  elementary 
knowledge  of  logarithms  is  required,  but  sufficient  for  the 
purpose  can  be  gained  by  the  student,  if  necessary,  from 
a  few  hours'  study  of  the  chapter  on  "  Logarithms "  in 
any  elementary  text-book  on  Algebra. 

The  experiments  described  in  the  sections  headed 
"  Practical  Illustrations  "  at  the  conclusion  of  the  chap- 
ters can  in  most  cases  be  performed  with  very  simple 
apparatus,  and  as  many  as  possible  should  be  done  by 
the  student.  The  majority  of  them  are  also  well  adapted 
for  lecture  experiments.  The  more  elaborate  experi- 


PREFACE  v 

ments  which  are  usually  performed  during  a  course  of 
practical  Physical  Chemistry  are  also  mentioned  for  the 
sake  of  completeness ;  for  full  details  a  book  on  Practical 
Physical  Chemistry  should  be  consulted. 

In  drawing  up  my  lectures,  which  have  developed  into 
the  present  book,  I  have  been  indebted  most  largely  to 
the  text-books  of  my  former  teachers,  Ostwald  and 
Nernst,  more  particularly  to  Ostwald's  Allgemeine  Chemie 
(2nd  Edition,  Leipzig,  Engelmann)  and  to  Nernst's  Theo- 
retical Chemistry  (4th  Edition,  London,  Macmillan).1  The 
following  works,  among  others,  have  also  been  consulted  : 
Van't  Hoff,  Lectures  on  Physical  Chemistry  ;  Arrhenius, 
Theories  of  Chemistry  ;  Le  Blanc,  Electrochemistry;  Dan- 
neel,  Elektrochemie  (Sammlung  Goschen) ;  Roozeboom, 
Phasenlehre ;  Findlay,  The  Phase  Rule;  Mel  lor,  Chemi- 
cal Statics  and  Dynamics ;  Abegg,  Die  elektrolytische 
Dissociationstheorie.  In  these  books  the  student  will 
find  fuller  treatment  of  the  different  branches  of  the 
subject.  References  to  other  sources  of  information  on 
particular  points  are  given  throughout  the  book. 

The  importance  of  a  study  of  original  papers  can 
scarcely  be  overrated,  and  I  have  given  references  to  a 
number  of  easily  accessible  papers,  both  in  English  and 
German,  some  of  which  should  be  read  even  by  the 
beginner.  In  the  summarising  chapter  on  "  Theories  of 
Solution"  references  are  given  which  will  enable  the 
more  advanced  student  to  put  himself  abreast  of  the  pre- 
sent state  of  knowledge  in  this  most  interesting  subject. 

In  conclusion,  I  wish  to  express  my  most  sincere 
thanks  to  Assistant-Professor  A.  W.  Porter,  of  University 

1  The  fifth  German  edition  of  Nernst's  text-book  has  now  appeared. 


vi          OUTLINES  OF  PHYSICAL  CHEMISTRY 

College,  London,  for  reading  and  criticising  the  sections 
on  osmotic  pressure  and  allied  phenomena,  and  for  valu- 
able advice  and  assistance  on  many  occasions ;  also 
to  Dr.  H.  Sand,  of  University  College,  Nottingham,  and 
Dr.  A.  Slator,  of  Burton,  for  criticising  the  chapters  on 
Electromotive  Force  and  on  Velocity  of  Reaction  respec- 
tively. Lastly,  I  wish  to  acknowledge  my  indebtedness 
to  my  assistant,  Mr.  T.  J.  Ward,  in  the  preparation  of  the 
diagrams  and  for  reading  the  proofs. 

G.   S. 

November,  1908 


PREFACE   TO   SECOND   EDITION 

AS  less  than  two  years  have  elapsed  since  the  appear- 
ance of  the  First  Edition,  only  a  few  slight  altera- 
tions have  been  rendered  necessary  by  the  progress  of 
the  subject  in  the  interval.  The  opportunity  has,  how- 
ever, been  taken  to  revise  the  text  thoroughly ;  in  one 
or  two  places  the  wording  has  been  slightly  altered  for 
the  sake  of  greater  clearness,  and  some  misprints  have 
been  corrected. 

A  few  additions  of  some  importance  have  also  been 
made.  In  conformity  with  the  elementary  character  of 
the  book,  the  mathematical  proofs  of  the  connection  be- 
tween osmotic  pressure  and  the  other  properties  of  solu- 
tions which  can  be  made  use  of  for  molecular  weight 
determinations  were  omitted  from  the  first  edition.  The 
book  has,  however,  been  more  largely  used  by  advanced 
students  than  was  anticipated,  and  at  the  request  of 
several  teachers  the  proofs  in  question  have  now  been 
inserted — as  an  appendix  to  chapter  V.  The  section 
dealing  with  the  relationship  between  physical  properties 
and  chemical  constitution  has  been  rendered  more  com- 
plete by  the  insertion  of  brief  accounts  of  absorption 
spectra  and  of  viscosity. 


viii        OUTLINES  OF  PHYSICAL  CHEMISTRY 

I  am  again  indebted  to  Professor  Porter  for  much 
kind  advice  and  assistance,  and  take  this  opportunity  of 
expressing  to  him  my  grateful  thanks.  I  wish  also  to 
acknowledge  my  indebtedness  to  a  number  of  friends  and 
correspondents,  more  particularly  to  Dr.  A.  Lapworth, 
F.R.S.,  Dr.  J.  C.  Philip,  Dr.  A.  E.  Dunstan,  Dr.  W. 
Maitland  and  Mr.  W.  G.  Pirie,  M.A.,  for  valuable  sug- 
gestions. 

G.  S. 


December,  1910. 


PREFACE  TO  THIRD  EDITION 

THE  fact  that  a  new  edition  is  called  for  so  soon  after 
the  appearance  of  the  previous  one  shows  that 
the  object  with  which  the  book  was  written — to  assist  in 
spreading  a  knowledge  of  the  principles  and  methods  of 
Physical  Chemistry — is  being  satisfactorily  fulfilled.  The 
present  opportunity  has  been  taken  to  add  certain  new 
sections,  with  the  object  of  further  increasing  the  useful- 
ness of  the  book. 

The  most  important  addition  is  a  new  chapter  on 
Colloidal  Solutions.  This  subject  has  developed  so 
rapidly  in  recent  years  that  the  couple  of  pages  devoted 
to  it  in  the  previous  editions  had  become  quite  inadequate. 
As  the  discussion  of  colloidal  problems  requires  a  know- 
ledge of  osmotic  and  electrical  measurements,  the  new 
chapter  has  been  placed  towards  the  end  of  the  book. 

The  other  important  addition  is  a  selection  of  num- 
erical problems  for  solution.  In  the  Preface  to  the  First 
Edition,  the  great  educational  value  of  numerical  examples 
was  emphasized,  and  further  experience  has  served  to 
confirm  and  strengthen  the  opinion  then  stated.  I  had 
intended  to  insert  a  number  of  numerical  problems  in  the 
Second  Edition,  but  pressure  of  other  work  prevented 
this  intention  being  fulfilled  till  the  present.  Within  the 
last  few  months,  two  very  useful  books  dealing  with 
Physico-Chemical  Calculations  have  been  published,  and 
in  these  the  student  will  find  further  examples  and 
exercises. 

G.  S. 

July,  19 13 

ix 


TABLE  OF  CONTENTS 

(The  numbers  refer  to  pages) 

CHAPTER  I 

PAGE 

FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY. 

THE  ATOMIC  THEORY  i 

Elements  and  compounds,  i — Laws  of  chemical  combination,  3 
— Atoms  and  molecules,  5 — Fact.  Generalisation  or  natural 
law.  Hypothesis.  Theory,  6 — Determination  of  atomic 
weights.  General,  8— Volumetric  method.  Gay-Lussac's 
law  of  volumes.  Avogadro's  hypothesis,  9 — Dulong  and 
Petit's  law,  n — Isomorphism,  13 — Determination  of  atomic 
weights  by  chemical  methods,  14 — Relation  between  atomic 
weights  and  chemical  equivalents.  Valency,  15 — The  values 
of  the  atomic  weights,  16 — The  periodic  system,  20. 

CHAPTER  II 
GASES .        .       25 

The  gas  laws,  25— Deviations  from  the  gas  laws,  28 — Kinetic 
theory  of  gases.  General,  29 — Kinetic  equation  for  gases, 
30 — Deduction  of  gas  laws  from  the  equation  pv  =  ^mnc2, 
31 — Van  der  Waals'  equation,  33 — Avogadro's  hypothesis 
and  the  molecular  weight  of  gases.  General,  36 — Density 
and  molecular  weight  of  gases  and  vapours,  36 — Results 
of  vapour  density  determinations.  Abnormal  molecular 
weights,  40 — Association  and  dissociation  in  gases,  41 — Ac- 
curate determination  of  molecular  and  atomic  weights  from 
gas  densities,  42 — Specific  heat  of  gases.  General,  43 — 
xi 


xii          OUTLINES  OF  PHYSICAL  CHEMISTRY 

PACK 

Specific  heat  at  constant  pressure,  Cp,  and  constant  volume, 
Cv,  44 — Specific  heat  of  gases  and  the  kinetic  theory,  46  — 
Experimental  illustrations,  47. 

CHAPTER  III 
LIQUIDS  .  .  ....      49 

General,  49— Transition  from  gaseous  to  liquid  state.  Critical 
phenomena,  49 — Behaviour  of  gases  on  compression,  51 — 
Application  of  Van  der  Waals'  equation  to  critical  pheno- 
mena, 53 — Law  of  corresponding  states,  56 — Liquefaction  of 
gases,  58 — Relation  between  physical  properties  and  chemi- 
cal composition  of  liquids.  General,  59 — Atomic  and  mole- 
cular volumes,  60 — Additive,  constitutive,  and  colligative 
properties,  62 — Retractivity,  63 — Rotation  of  plane  of 
polarization  of  light,  66 — Absorption  of  light,  69 — Viscosity, 
73— Practical  illustrations,  77 

CHAPTER  IV 
SOLUTIONS 80 

General  80 — Solution  of  gases  in  gases,  81 — Solubility  of  gases 
in  liquids,  82 — Solubility  of  liquids  in  liquids,  84 — Distilla- 
tion of  homogeneous  mixtures,  87 — Distillation  of  non- 
miscible  or  partially  miscible  liquids ;  steam  distillation,  go — 
Solution  of  solids  in '  liquids,  91 — Effect  of  change  of  tem- 
perature on  the  solubility  of  solids  in  liquids,  92 — Relation 
between  solubility  and  chemical  constitution,  94 — Solid 
solutions,  94 — Practical  illustrations,  95. 

CHAPTER  V 

DILUTE  SOLUTIONS      .  ...      97 

General,  97 — Osmotic  pressure.  Semi-permeable  membranes, 
97 — Measurement  of  osmotic  pressure,  99 — Van't  Hoff's 
theory  of  solution,  101 — Recent  direct  measurements  of 
osmotic  pressure,  104 — Other  methods  of  determining  osmo- 
tic pressure,  105 — Mechanism  of  osmotic  pressure,  106 — 
Osmotic  pressure  and  diffusion,  108 — Molecular  weight  of 
dissolved  substances.  General,  109 — Molecular  weights 


TABLE  OF  CONTENTS  xiii 

PACS 

from  osmotic  pressure  measurements,  no — Lowering  of 
vapour  pressure,  in — Elevation  of  boiling-point,  114 — Ex- 
perimental determination  of  molecular  weights  by  the 
boiling-point  method,  116 — Depression  of  the  freezing-point, 
119 — Experimental  determination  of  molecular  weights  by 
the  freezing-point  method,  120— Results  of  molecular  weight 
determinations  in  solution.  General,  121 — Abnormal  mole- 
cular weights,  123 — Molecular  weight  of  liquids,  125 — The 
results  of  measurements,  127 — Nature  of  surface  tension, 
129 — Practical  illustrations,  129.  Mathematical  deduction 
of  formulae,  131. 

CHAPTER  VI 
THERMOCHEMISTRY  .  ...     139 

General,  139 — Hess's  law,  141 — Representation  of  thermo- 
chemical  measurements.  Heat  of  formation,  143 — Heat  of 
combustion,  145 — Thermochemical  methods,  145 — Results 
of  thermochemical  measurements,  147 — Relation  of  chemi- 
cal affinity  to  heat  of  reaction,  148 — Practical  illustrations, 
153- 

CHAPTER    VII 
EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS. 

LAW  OF  MASS  ACTION  .         .         .         .     I54 

General,  154 — Law  of  mass  action,  155 — Strict  proof  of  the  law 
of  mass  action,  160 — Decomposition  of  hydriodic  acid,  161 
— Dissociation  of  phosphorus  pentachloride,  163 — Equili- 
brium in  solutions  of  non-electrolytes,  164 — Influence  of 
temperature  and  pressure  on  chemical  equilibrium.  General, 
166 — Le  Chatelier's  theorem,  169 — Relation  between  chemi- 
cal equilibrium  and  temperature.  Nernst's  views,  169 
Practical  illustrations,  170. 

CHAPTER    VIII 
HETEROGENEOUS  EQUILIBRIUM.    THE  PHASE 

RULE          .  ,72 

General,    172 — Application   of  law  of  mass   action    to   hetero- 
geneous equilibrium,  172— Dissociation  of  salt  hydrates,  174 
b 


xiv          OUTLINES  OF  PHYSICAL  CHEMISTRY 

PAGE 

— Dissociation  of  ammonium  hydrosulphide,  176 — Analogy 
between  solubility  and  dissociation,  177 — Distribution  of  a 
solute  between  two  immiscible  liquids,  177 — The  phase  rule. 
Equilibrium  between  water,  ice  and  steam,  179 — Equilibrium 
between  four  phases  of  the  same  substance.  Sulphur,  183 
— Systems  of  two  components.  Salt  and  water,  186 — 
Freezing  mixtures,  189 — Systems  of  two  components. 
General,  190 — Hydrates  of  ferric  chloride,  194 — Transition 
points,  197 — Practical  illustrations,  197. 

CHAPTER  IX 
VELOCITY  OF  REACTION.     CATALYSIS     .         .200 

General,  200 — Unimolecular  reaction,  202 — Other  unimolecular 
reactions,  205 — Bimolecular  reactions,  207 — Trimolecular 
reactions,  209 — Reactions  of  higher  order.  Molecular- 
kinetic  considerations,  211 — Reactions  in  stages,  212 — 
Determination  of  the  order  of  a  reaction,  213 — Complicated 
reaction  velocities,  215 — Catalysis.  General  ,217 — Charac- 
teristics of  catalytic  actions,  217 — Examples  of  catalytic 
action.  Technical  importance  of  catalysis,  219 — Biological 
importance  of  catalysis.  Enzyme  reactions,  221 — Mechan- 
ism of  catalysis,  222 — Nature  of  the  medium,  224 — Influence 
of  temperature  on  the  rate  of  chemical  reaction,  225 — 
Formulae  connecting  reaction  velocity  and  temperature,  228 
— Practical  illustrations,  229. 

CHAPTER  X 
ELECTRICAL  CONDUCTIVITY     .  .    234 

General,  234 — Electrolysis  of  solutions.  Faraday's  laws,  236— 
Mechanism  of  electrical  conductivity,  238 — Freedom  of  the 
ions  before  electrolysis,  240 — Dependence  of  conductivity  on 
the  number  and  nature  of  the  ions,  242 — Migration  velocity 
of  the  ions,  243— Practical  determination  of  the  relative 
migration  velocities  of  the  ions,  246 — Specific,  molecular 
and  equivalent  conductivity,  249— Kohlrausch's  law.  Ionic 
velocities,  251 — Absolute  velocity  of  the  ions.  Internal 


TABLE  OF  CONTENTS  xv 

PAGE 

friction,  253 — Experimental  determination  of  conductivity  of 
electrolytes,  254 — Experimental  determination  of  molecular 
conductivity,  257 — Results  of  conductivity  measurements, 
258 — Electrolytic  dissociation,  260 — Degree  of  ionisation 
from  conductivity  and  osmotic  pressure  measurements,  261 
— Effect  of  temperature  on  conductivity,  263 — Practical 
illustrations,  264. 

CHAPTER  XI 

EQUILIBRIUM  IN  ELECTROLYTES.  STRENGTH 

OF  ACIDS  AND  BASES.     HYDROLYSIS         .    266 

The  dilution  law,  266— Strength  of  acids,  269 — Strength  of 
bases,  274 — Mixture  of  two  electrolytes  with  a  common  ion, 
276 — Isohydric  solutions,  277 — Mixture  of  electrolytes  with 
no  common  ion,  278 — Dissociation  of  strong  electrolytes, 
279 — Electrolytic  dissociation  of  water.  Heat  of  neutrali- 
sation, 283 — Hydrolysis,  285 — Hydrolysis  of  the  salt  of  a 
strong  base  and  a  weak  acid,  287 — Hydrolysis  of  the  salt 
of  a  weak  base  and  a  strong  acid,  290 — Hydrolysis  of  the 
salt  of  a  weak  base  and  a  weak  acid,  292 — Determination  of 
the  dissociation  constant  for  water,  293 — Theory  of  indica- 
tors, 296 — The  solubility  product,  298 — Applications  to 
analytical  chemistry,  300 — Experimental  determination  of 
the  solubility  of  difficultly  soluble  salts,  301 — Complex  ions, 
303 — Influence  of  substitution  on  degree  of  ionisation, 
304 — Reactivity  of  the  ions,  306 — Practical  illustrations, 
307- 

CHAPTER    XII 
COLLOIDAL  SOLUTIONS.      ADSORPTION.         .     313 

Colloidal  solutions.  General,  313 — Preparation  of  colloidal  solu- 
tions, 315—  Osmotic  pressure  and  molecular  weight  of 
colloids,  316— Optical  properties  of  colloidal  solutions,  317 
— Brownian  movement,  318 — Electrical  properties  of  col- 
loids, 319— Precipitation  of  colloids  by  electrolytes,  320— 


xvi        OUTLINES  OF   PHYSICAL   CHEMISTRY 

Suspensions,  suspensoids  and  emulsoids,  322 — Filtration  of 
colloidal  solutions,  323 — Adsorption,  general,  324 — Adsorp- 
tion of  gases.  Adsorption  formulae,  328 — The  cause  of 
adsorption,  329 — Further  illustrations  of  adsorption,  330. 

CHAPTER   XIII 
THEORIES  OF  SOLUTION 333 

General,  333 — Evidence  in  favour  of  the  electrolytic  dissociation 
theory,  335 — lonisation  in  solvents  other  than  water,  337 — 
The  old  hydrate  theory  of  solution,  339 — Mechanism  of 
electrolytic  dissociation.  Function  of  the  solvent,  342 — 
Hydration  in  solution,  345. 

CHAPTER   XIV 

ELECTROMOTIVE  FORCE    .....     348 

The  Daniel  cell,  348— Relation  between  chemical  and  electrical 
energy,  351 — Measurement  of  electromotive  force,  354— 
Standard  of  electromotive  force.  The  cadmium  element, 
356 — Solution  pressure,  358 — Calculation  of  electromotive 
force  at  a  junction  metal/salt  solution,  360 — Differences  of 
potential  in  a  voltaic  cell,  362 — Influence  of  change  of  con- 
centration of  salt  solution  on  the  E.M.F.  of  a  cell,  365 — 
Concentration  cells,  367 — Cells  with  different  concentrations 
of  the  electrode  materials  (substances  producing  ions),  371 — 
Electrodes  of  the  first  and  second  kind.  The  calomel  elec- 
trode, 373 — Single  potential  differences.  The  capillary 
electrometer,  378 — Potential  differences  at  junction  of  two 
liquids,  382— Gas  cells,  384 — Potential  series  of  the  ele- 
ments, 386 — Cells  with  different  gases,  389 — Oxidation- 
reduction  cells,  390 — Electrolysis  and  polarization,  393 — 
Separation  of  ions  (particularly  of  metals)  by  electrolysis, 
395 — The  electrolysis  of  water,  396— Accumulators,  397 — 
The  electron  theory,  398 — Practical  illustrations,  401. 


DEFINITIONS  AND   UNITS1 

In  this  section  the  centimetre-gram-second  (C.G.S.)  system  of  units 
is  used  throughout,  length  being  measured  in  centimetres  (cms.),  mass  in 
grams,  and  time  in  seconds. 

Density  is  mass  per  unit  volume  :  unit,  gram  per  c.c.  (cubic  centi- 
metre). 

Specific  Volume  (i/density)  is  .volume  per  unit  mass :  unit,  c.c.  per 
gram. 

Velocity  is  rate  of  change  of  position  :  unit,  cm.  per  sec.  or  cm. /sec. 

Acceleration  is  rate  of  change  of  velocity  :  unit,  cm.  per  sec.  per  sec. 
or  cm./sec.2. 

Momentum  is  mass  x  velocity  :  unit,  gram-cm,  per  sec. 

Force  is  mass  x  acceleration  (rate  of  change  of  momentum).  Unit, 
the  dyne,  is  that  force  which  is  required  to  produce  an  acceleration  of  I  cm. 
per  sec.  per  sec.  in  a  mass  of  i  gram.  As  a  gram-weight,  falling  freely, 
obtains  an  acceleration  of  980-6  cm.  per  sec.  (owing  to  the  attraction  of 
the  earth)  the  force  represented  by  the  gram-weight  =  g&o'6  dynes  at 
a  latitude  of  45°  and  at  sea-level. 

Energy  may  be  defined  as  that  property  of  a  body  which  diminishes 
when  work  is  done  by  the  body ;  and  its  diminution  is  measured  by  the 
amount  of  work  done. 

Work  Done  is  force  x  distance  (the  work  done  by  a  force  is  measured 
by  the  product  of  the  force  and  the  distance  through  which  the  point  of 
application  moves  in  the  direction  of  the  force).  The  unit  of  work 

1  The  more  important  constants  made  use  of  in  physical  chemistry 
are  collected  here  for  convenience  of  reference. 

xvii 


xviii       OUTLINES  OF  PHYSICAL  CHEMISTRY 

(which  is  also  the  unit  of  energy)  is  the  dyne-centimetre  or  erg.  The 
gram-centimetre  unit  is  sometimes  used ;  i  gram-centimetre  =  980-6 
ergs ;  also  the  joule  (=  io7  ergs)  is  frequently  used,  especially  in  electrical 
work  (see  below). 

Power  is  rate  of  doing  work,  unit,  erg  per  second. 

There  are  six  chief  forms  of  energy:  (i)  mechanical  energy,  (2) 
volume  energy,  (3)  electrical  energy,  (4)  heat,  (5)  chemical  energy,  (6) 
radiant  energy.  These  forms  of  energy  are  mutually  convertible,  and 
according  to  the  law-  of  conservation  of  energy,  there  is  a  definite  and 
invariable  relationship  between  the  quantity  of  one  kind  of  energy  which 
disappears  and  that  which  results. 

The  unit  of  energy,  the  erg,  has  already  been  defined.  It  is  some- 
times convenient  to  express  certain  forms  of  energy  in  special  units,  heat» 
for  example,  in  calories ;  in  the  following  paragraphs  the  equivalents  in 
ergs  of  these  special  units  are  given. 

Volume  Energy  is  often  measured  in  litre-atmospheres.  When  a 
volume,  Wj,  of  a  gas  expands  to  the  volume  v2  against  a  constant  pressure 
p,  say  that  of  the  atmosphere,  the  external  work  done  by  the  gas  (gained) 
is  p  (v%  -  vj.  The  (average)  pressure  of  the  atmosphere  on  unit  area 
(i  sq.  cm.)  supports  a  column  of  mercury  76  cm.  high  and  i  sq.  cm.  in 
cross-section.  Hence  the  pressure  on  i  sq.  cm.  =  76  x  13*596  =  1033-3 
grams  weight  (as  the  density  of  mercury  is  I3'596),  or  1033*3  x  980-6  = 
1,013,200  dynes.  As  the  work  done  is  the  product  of  the  constant  pres- 
sure and  the  increase  of  volume,  i  litre-atmosphere  (the  work  done  when 
the  increase  in  the  volume  of  a  certain  quantity  of  a  gas  is  i  litre  or 
1000  c.c.)  =  1,013,200  x  1000  =  1,013,200,000  ergs. 

Electrical  Energy  is  the  product  of  electromotive  force  and  quantity 
of  electricity,  and  is  usually  measured  in  volt-coulombs  or  joules.  The 
practical  unit  of  quantity  of  electricity  is  the  coulomb ;  it  is  that  quantity 
of  electricity  which  under  certain  conditions  liberates  o'ooniS  grams  of 
silver  from  a  solution  of  silver  nitrate.  If  a  coulomb  passes  through  a 
conductor  in  i  second,  the  strength  of  current  is  i  ampere ;  the  latter  is 
therefore  the  practical  unit  of  strength  of  current.  The  practical  unit  of 
resistance  is  the  ohm,  which  is  the  resistance  at  o°  offered  by  a  column  of 
mercury  106*3  cm.  long  and  weighing  14-4521  grams.  The  practical  unit 
of  electromotive  force  is  the  volt ;  when  a  current  of  i  ampere  passes  in 
i  second  through  a  conductor  of  resistance  i  ohm,  the  electromotive 
force  is  i  volt. 


DEFINITIONS  AND  UNITS  xix 

The  definitions  of  the  C.G.S.  units  of  electromotive  force,  current 
strength  and  resistance  are  to  be  found  in  text-books  of  physics,  and 
cannot  be  given  here.  It  can  be  shown  that  i  ohm  =  io9  C.G.S.  units 
and  i  ampere  =  i/io  C.G.S.  unit;  hence,  by  Ohm's  law,  i  volt  =  10^ 
C.G.S.  units.  Further,  i  volt-coulomb  or  i  joule  =  io8  x  io-1  =  io* 
C.G.S.  units  or  io7  ergs. 

Heat  Energy  is  measured  in  calories.  The  mean  calorie  is  i/ioo  of 
the  amount  of  heat  required  to  raise  i  gram  of  water  from  o  to  100°  and 
does  not  differ  much  from  the  amount  of  heat  required  to  raise  i  gram  of 
water  from  15°  to  16°.  i  calorie  =  42,650  gram-centimetres  =  41,830,000 
ergs  (the  mechanical  equivalent  of  heat)  =  4*183  joules.  One  joule  = 
0*2391  calories.  There  is  no  special  unit  for  chemical  energy;  it  is 
usually  measured  in  volt-coulombs  or  calories. 

TTie  value  of  R,  in  the  general  gas  equation  (p.  27)  for  a  mol  of  gas  = 
54,760  gram-centimetres  =  83,150,000  ergs  =  8-315  joules  =  1*985  calories 
=  0*08205  litre-atmospheres. 

USE  OF  SIGNS  IN  ELECTRO-CHEMISTRY. 
There  has  always  been  much  confusion  in  Electro-chemistry  as  to  the 
proper  use  of  positive  and  negative  signs,  and  even  now  no  general 
agreement  has  been  reached  on  the  subject.  Recently,  however,  a  simple 
convention  has  been  suggested  by  the  German  Electro-chemical  Society 
(Bunsen-Gesellschaft)  which  promises  to  find  general  acceptance.  The 
potential  difference  has  the  positive  sign  if  the  metal  is  charged  positively 
with  respect  to  the  solution,  and  negative  if  the  metal  is  negatively 
charged,  when  metal  and  solution  are  combined  with  a  comparison 
electrode  to  form  a  cell  (cf.  p.  358).  In  the  present  book,  while  this  con- 
vention is  adopted  for  the  potential  series  of  the  elements,  etc.,  the 
potential  differences  are  often  given  in  absolute  value  and  the  E.M.F.  of 
combinations  illustrated  by  the  graphic  method  described  on  pp.  365,  377, 
386  and  elsewhere.  As  a  result  of  considerable  experience,  it  has  been 
found  that  the  graphic  method  is  much  more  useful  in  avoiding  errors  of 
sign  than  any  convention  with  regard  to  the  use  of  signs. 


OUTLINES  OF 
PHYSICAL  CHEMISTRY 

CHAPTER  I 

FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY. 
THE  ATOMIC  THEORY 

Elements  and  Compounds — Definite  chemical  substances 
are  divided  into  the  two  classes  of  elements  and  chemical  com- 
pounds.  Boyle,  and  later  Lavoisier,  defined  an  element  as  a 
substance  which  had  not  so  far  been  split  up  into  anything 
simpler.  The  substances  formed  by  chemical  combination  of 
two  or  more  elements  were  termed  chemical  compounds. 
This  definition  proved  to  be  a  very  suitable  one,  and  retained 
its  value  even  when  many  of  the  substances  classed  as  ele- 
ments by  Lavoisier  proved  to  be  complex.  In  course  of 
time  it  came  to  be  recognised  that  the  substances  which  resisted 
further  decomposition  possessed  certain  other  properties  in  com- 
mon, for  example,  the  so-called  atomic  heat  of  solid  elements 
proved  to  be  approximately  6*4  (p.  12),  and  it  was  found  possible 
to  assign  even  newly-discovered  elements  with  more  or  less 
certainty  to  their  appropriate  positions  in  the  periodic  table  of 
the  elements  p.  21).  There  are,  therefore,  conclusive  reasons, 
apart  from  the  fact  that  they  have  so  far  resisted  decomposi- 
tion, for  regarding  elements  as  of  a  different  order  from  chemical 
compounds,  and  these  reasons  remain  equally  valid  when  full 
allowance  is  made  for  the  remarkable  discoveries  of  the  last 
few  years  in  this  branch  of  knowledge. 


2  OUTLINES  OF  PHYSICAL  CHEMISTRY 

Until  lately  no  case  of  the  transformation  of  one  element  into 
another  was  known,  but  recent  work  on  radium,  by  Ramsay  and 
Soddy  and  others,  has  shown  that  this  element  is  continuously 
undergoing  a  series  of  transformations,  one  of  the  final  products 
of  which  is  the  inactive  gas  helium.  It  might  at  first  sight  be 
supposed  that  the  old  view  of  the  impossibility  of  transforming 
the  elements  could  be  maintained,  radium  being  looked  upon 
as  a  chemical  compound  of  helium  with  another  element,  but 
further  consideration  shows  that  this  suggestion  is  not  tenable, 
as  radium  fits  into  the  periodic  table,  and,  so  far  as  is  known, 
possesses  all  those  other  properties  which  have  so  far  been  con- 
sidered characteristic  of  elements  as  distinguished  from  chemical 
compounds. 

Evidence  is  gradually  accumulating  which  indicates  that  the 
slow  disintegration,  with  final  production  of  other  elements,  is 
not  confined  to  radium  alone,  but  is  shown  more  particularly 
by  certain  elements  of  high  atomic  weight  such  as  uranium  and 
thorium.  It  is  true  that  the  change  is  spontaneous,  as  so  far 
there  is  no  known  means  of  initiating  it  or  even  of  influencing 
its  rate,  but  further  progress  in  this  direction  is  doubtless  only 
a  matter  of  time.  As  the  phenomenon  in  question  is  probably 
a  general  one,  it  seems  desirable  to  retain  the  term  "  element " 
to  indicate  a  substance  which  has  a  definite  position  in  the 
periodic  table,  and  has  the  other  properties  usually  regarded  as 
characteristic  of  elements. 

From  what  has  been  said,  it  will  be  evident  that  it  is  difficult 
to  define  an  element  in  a  few  words,  but  in  practice  there  will 
probably  not  be  much  difficulty  in  drawing  the  distinction 
between  elements  and  compounds.  Ostwald 1  (1907)  defines  an 
element  as  a  substance  which  only  increases  in  weight  as  the 
result  of  a  chemical  change,  and  which  is  stable  under  any 
attainable  conditions  of  temperature  and  pressure,  but  in  this 
definition  the  question  of  radio-active  substances  is  left  out  of 
account. 

iprinzipien  der  Chemie,  Leipzig,  1907,  p.  266. 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     3 

Laws  of  Chemical  Combination — Towards  the  end  of 
the  eighteenth  century,  Lavoisier  established  experimentally 
the  law  of  the  conservation  of  mass,  which  may  be  expressed 
as  follows :  When  a  chemical  change  occurs,  the  total  weight 
(or  mass)  of  the  reacting  substances  is  equal  to  the  total  weight 
(or  mass]  of  the  products.  As  the  weight  is  proportional  to 
the  mass  or  quantity  of  matter,  the  above  law  may  also  be 
stated  in  the  form  that  the  total  quantity  of  matter  in  the  uni- 
verse is  not  altered  in  consequence  of  chemical  (or  any  other) 
changes.  It  is,  of  course,  impossible  to  prove  the  law  with 
absolute  certainty,  but  the  fact  that  in  accurate  atomic  weight 
determinations  no  results  in  contradiction  with  it  have  been 
obtained  shows  that  it  is  valid  at  least  within  the  limits  of  the 
unavoidable  experimental  error. 

The  enunciation  of  the  law  of  the  conservation  of  mass  by 
Lavoisier,  and  the  extended  use  of  the  balance,  facilitated  the 
investigation  of  the  proportions  in  which  elements  combine,  and 
soon  afterwards  the  first  law  of  chemical  combination  was  estab- 
lished by  the  careful  experimental  investigations  of  Richter  and 
Proust.  This  law  is  usually  expressed  as  follows  : — 

A  definite  compound  always  contains  the  same  elements  in  the 
same  proportions. 

The  truth  of  this  law  was  called  in  question  by  the  famous 
French  chemist  Berthollet.  Having  observed  that  chemical 
processes  are  greatly  influenced  by  the  relative  amounts  of 
the  reacting  substances  (p.  155),  he  contended  that  when,  for 
example,  a  chemical  compound  is  formed  by  the  combination 
of  two  elements,  the  proportion  of  one  of  the  elements  in  the 
compound  will  be  the  greater  the  more  of  that  element  there 
is  available.  This  suggestion  led  to  the  famous  controversy 
between  Berthollet  and  Proust  (1799-1807),  which  ended  in 
the  firm  establishment  of  the  law  of  constant  proportions.  All 
subsequent  work  has  shown  that  the  law  in  question  is  valid 
within  the  limits  of  experimental  error. 

In  certain  cases,  elements  unite  in  more  than  one  proportion 


4  OUTLINES  OF  PHYSICAL  CHEMISTRY 

to  form  definite  chemical  compounds.  Thus  Dalton  found  by 
analysis  that  two  compounds  of  carbon  and  hydrogen — methane 
and  ethylene — contain  the  elements  in  the  ratios  6  :  2  and  6  :  i 
by  weight  respectively ;  in  other  words,  for  the  same  amount  of 
carbon,  the  amounts  of  hydrogen  are  in  the  ratio  2:1.  Similar 
simple  relations  were  observed  for  other  compounds,  and  on 
this  experimental  basis  Dalton  (1808)  formulated  the  Law  of 
Multiple  Proportions,  as  follows : — 

When  two  elements  unite  in  more  than  one  proportion,  for  a 
fixed  amount  of  one  element  there  is  a  simple  ratio  between  the 
amounts  of  the  other  element. 

Dalton's  experimental  results  were  not  of  a  high  order  of 
accuracy,  but  the  validity  of  the  law  was  proved  by  the 
subsequent  investigations  of  Berzelius,  Marignac  and  others. 

Finally,  there  is  a  third  comprehensive  law  of  combination, 
which  includes  the  other  two  as  special  cases.  It  has  been 
found  possible  to  ascribe  to  each  element  a  definite  relative 
weight,  with  which  it  enters  into  chemical  combination.  The 
Law  of  Combining  Proportions,  which  expresses  this  conception, 
is  as  follows  : — 

Elements  combine  in  the  ratio  of  their  combining  weights,  or  in 
simple  multiples  of  this  ratio. 

The  combining  weights  are  found  by  analysis  of  definite  com- 
pounds containing  the  elements  in  question.  When  the  com- 
bining weight  of  hydrogen  is  taken  as  unity,  the  approxi- 
mate values  for  chlorine,  oxygen  and  sulphur  are  35*5,  8  and 
1 6  respectively.  These  numbers  also  represent  the  ratios  in 
which  the  elements  displace  each  other  in  chemical  com- 
pounds. Water,  for  example,  contains  8  parts  by  weight  of 
oxygen  to  i  of  hydrogen,  and  when  the  former  element  is  dis- 
placed by  sulphur  (forming  hydrogen  sulphide)  the  new  com- 
pound is  found  to  contain  16  parts  by  weight  of  the  latter 
element.  1 6  parts  of  sulphur  are  therefore  equivalent  to  8  parts 
of  oxygen,  and  the  combining  weights  are  therefore  often  termed 
chemical  equivalents-  The  chemical  equivalent  of  an  element  is. 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     5 

that  quantity  of  it  which  combines  with,  or  displaces,  one  part 
(strictly  1*008  parts)  by  weight  of  hydrogen  (cf.  p.  18). 

It  must  be  clearly  understood  that  the  above  generalisations 
or  laws  are  purely  experimental ;  they  express  in  a  simple  form 
the  results  of  the  investigations  of  many  chemists  on  the  com- 
bining powers  of  the  elements,  and  are  quite  independent  of 
any  hypothesis  as  to  the  constitution  of  matter.  As  they  have 
been  established  by  experiment,  we  are  certain  of  their  validity 
only  within  the  limits  of  the  unavoidable  experimental  error, 
and  cannot  say  whether  they  are  absolutely  true.  It  is  possible 
that  when  the  methods  of  analysis  are  greatly  improved,  it  will 
be  possible  to  detect  small  variations  in  the  composition  of 
definite  compounds,  but  up  to  the  present  the  most  careful 
investigations,  in  the  course  of  atomic  weight  determinations, 
have  failed  to  show  any  deviation  from  the  results  to  be  expected 
according  to  the  laws. 

Atoms  and  Molecules — The  question  now  arises  as  to 
whether  a  theory  can  be  suggested  which  allows  of  a  convenient 
and  consistent  representation  of  the  laws  enunciated  above. 
The  atomic  theory,  first  brought  forward  in  its  modern  form  by 
Dalton  (1808),  answers  these  requirements.  Following  out  an 
idea  of  the  old  Greek  philosophers,  Dalton  suggested  that 
matter  is  not  infinitely  divisible  by  any  means  at  our  disposal, 
but  is  made  up  of  extremely  small  particles  termed  atoms ;  the 
atoms  of  any  one  element  are  identical  in  all  respects  and 
differ,  at  least  in  weight,  from  those  of  other  elements.  By  the 
association  of  atoms  of  different  kinds,  chemical  compounds 
are  formed.  The  laws  of  chemical  combination  find  a  simple 
explanation  on  the  atomic  theory.  Since  a  chemical  compound 
is  formed  by  the  association  of  atoms,  each  of  which  has  a 
definite  weight,  it  must  be  of  invariable  composition.  Further 
when  atoms  combine  in  more  than  one  proportion,  for  a  fixed 
amount  of  atoms  of  one  kind  the  amount  of  the  other  must  in- 
crease in  steps,  depending  on  the  relative  atomic  weight — which 
is  the  law  of  multiple  proportions.  It  is  here  assumed  that 


6  OUTLINES  OF  PHYSICAL  CHEMISTRY 

the  ultimate  particles  of  a  compound  are  formed  by  the  associa- 
tion of  comparatively  few  atoms,  and  this  holds  in  general  for 
inorganic  compounds.  Finally,  the  law  of  combining  weights 
is  also  seen  to  be  a  logical  consequence  of  the  atomic  theory, 
the  empirically  found  combining  weights,  or  chemical  equiva- 
lents, bearing  a  simple  relation  to  the  (relative)  weights  of  the 
atoms  (p.  15). 

When  Dalton  brought  forward  the  atomic  theory,  the  number 
of  facts  which  it  had  to  account  for  was  comparatively  small. 
As  knowledge  has  progressed,  the  atomic  theory  has  proved 
capable  of  extension  to  represent  the  new  facts,  and  its  applica- 
tion has  led  to  many  important  discoveries.  At  the  present 
day,  the  great  majority  of  chemists  consider  that  the  atomic 
theory  has  by  no  means  outgrown  its  usefulness. 

Fact.  Generalisation  or  Natural  Law.  Hypothesis. 
Theory1 — Chemistry,  like  most  other  sciences,  is  based  on 
facts,  established  by  experiment.  A  few  such  facts  have  already 
been  mentioned,  for  example,  that  certain  chemical  compounds, 
which  have  been  investigated  with  the  greatest  care,  always 
contain  the  same  elements  in  the  same  proportions.  A  mere 
collection  of  facts,  however,  does  not  constitute  a  science. 
When  a  certain  number  of  facts  have  been  established,  the 
chemist  proceeds  to  reason  from  analogy  as  to  the  behaviour  of 
systems  under  conditions  which  have  not  yet  been  investigated. 
For  example,  Proust  showed  by  careful  analyses  that  there  are 
two  well-defined  oxides  of  tin,  and  that  the  composition  of 
each  is  invariable.  From  the  results  of  these  and  a  few  other 
investigations,  he  concluded  from  analogy  that  the  composition 
of  all  pure  chemical  compounds  is  invariable,  although  of  course 
very  few  of  them  had  then  been  investigated  from  that  point  of 
view.  To  proceed  in  this  way  is  to  generalise,  and  the  short 
statement  of  the  conclusion  arrived  at  is  termed  a  generalisation 

1  H.  Poincare",  La  Science  et  VHypothese,  Paris,  Flammarion  ;  Ostwald, 
Vorlesungen  uber  Naturphilosophie,  Leipzig,  1902;  Alexander  Smith, 
General  Inorganic  Chemistry,  London,  1906. 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     7 

or  law.  It  will  be  evident  that  a  law  is  not  in  the  nature  of  an 
absolute  certainty ;  it  comprises  the  facts  experimentally  estab- 
lished, but  also  enables  us  (and  herein  lies  its  value)  to  foretell  a 
great  many  things  which  have  not  been,  but  which  if  necessary 
could  be,  investigated  experimentally.  The  greater  the  number 
of  cases  in  which  a  law  has  been  found  to  hold,  the  greater  is  the 
confidence  in  its  validity,  until  finally  a  law  may  attain  practically 
the  same  standing  as  a  statement  of  fact.  We  may  confidently 
expect  that  however  greatly  our  views  regarding  natural  pheno- 
mena  may  change,  such  generalisations  as  the  law  of  constant 
proportions  will  remain  eternally  true. 

Natural  laws  can  be  discovered  in  two  ways :  (i)  by  corre- 
lating a  number  of  experimental  facts,  as  just  indicated  ;  (2)  by 
a  speculative  method,  on  the  basis  of  certain  hypotheses  as  to 
the  nature  of  the  phenomena  in  question.  The  meaning  to  be  at- 
tached to  the  term  "  hypothesis  "  is  best  illustrated  by  an  example. 
In  the  previous  section  we  have  seen  that  the  laws  of  chemical 
combination  are  accounted  for  satisfactorily  on  the  view  that 
matter  is  made  up  of  extremely  small,  discrete  particles,  the 
atoms.  Such  a  mechanical  representation,  which  is  more  or  less 
inaccessible  to  experimental  proof,  is  termed  a  hypothesis  A 
hypothesis  may  then  be  defined  as  a  mental  picture  of  an 
unknown,  or  largely  unknown,  state  of  affairs,  in  terms  of  some- 
thing which  is  better  known.  Thus,  the  state  of  affairs  in 
gases,  which  is  and  will  remain  unknown  to  us,  is  represented, 
according  to  the  kinetic  theory,  in  terms  of  an  enormous  number 
of  rapidly  moving  perfectly  elastic  particles,  and  on  this  basis 
it  is  possible,  with  the  help  of  certain  assumptions,  to  deduce 
certain  of  the  laws  which  are  actually  followed  by  gases  (p.  25). 

There  does  not  appear  to  be  any  fundamental  distinction  in 
the  use  of  the  terms  hypothesis  and  theory.  A  theory  may  be 
defined  as  a  hypothesis,  many  of  the  deductions  from  which 
have  been  confirmed  by  experiment,  and  which  admits  of  the  con- 
venient representation  of  a  large  number  of  experimental  facts. 

There   is1  some  difference   of  opinion   as   to    the   value    of 


8  OUTLINES  OF  PHYSICAL  CHEMISTRY 

hypotheses  and  theories  for  the  advancement  of  science.1  The 
majority  of  scientists,  however,  appear  to  consider  that  the 
advantages  of  hypotheses,  regarded  in  the  proper  light  and  not 
as  representing  the  actual  state  of  affairs,  are  much  greater  than 
the  disadvantages.  Boltzmann,2  indeed,  maintains  that  ''new 
discoveries  are  made  almost  exclusively  by  means  of  special 
mechanical  conceptions  ". 

DETERMINATION  OF  ATOMIC  WEIGHTS 

General — After  the  laws  of  chemical  combination  had  been 
established,  the  next  problem  with  which  chemists  had  to  deal 
was  the  determination  of  the  relative  atomic  weights  of  the 
elements.  This  might  apparently  be  done  by  fixing  on  one 
element,  say  hydrogen,  as  the  standard ;  a  compound  containing 
hydrogen  and  another  element  may  then  be  analysed,  and  the 
amount  of  the  other  element  combined  with  one  part  of  hydrogen 
will  be  its  atomic  weight.  It  is  clear,  however,  that  this  will 
be  the  case  only  when  the  binary  compound  contains  one  atom 
of  each  element,  and  it  was  just  this  difficulty  of  deciding  the 
relative  number  of  atoms  of  the  two  elements  present  that 
rendered  the  decision  between  a  number  and  one  of  its  multi- 
ples or  sub-multiples  so  difficult. 

It  has  already  been  pointed  out  that  the  amount  of  an  ele- 
ment which  combines  with,  or  displaces,  part  by  weight  of 
hydrogen  (strictly  speaking,  8  parts  by  weight  of  oxygen)  is 
termed  the  combining  weight  or  chemical  equivalent  of  an  ele- 
ment. The  first  step  in  determining  the  atomic  weight  of  an 
element  is  to  find  the  chemical  equivalent  as  accurately  as  pos- 
sible by  analysis  and  then  to  find  the  relation  between  the 
atomic  weight  and  chemical  equivalent  by  one  of  the  methods 
described  below.  The  atomic  weight  may  be  equal  to,  or  a 
simple  multiple  of,  the  chemical  equivalent. 

1  In  one  or  two  recent  books,  Ostwald  has  treated  certain  branches  of 
chemistry  on  a  system  free  from  hypotheses. 

2  Gas  Theorie,  Leipzig,  1896,  p.  4. 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     9 

Dalton,  working  on  the  assumption  that  when  two  elements 
unite  in  only  one  proportion  one  atom  of  each  is  present,  drew 
up  the  first  table  of  atomic  weights.  Water  was  found  by 
analysis  to  contain  i  part  of  hydrogen  to  8  parts  of  oxygen  by 
weight ;  the  atomic  weight  of  oxygen  was  therefore  taken  as  8. 
In  the  same  way,  since  ammonia  contained  i  part  of  hydrogen 
to  4'6  parts  of  nitrogen,  the  atomic  weight  of  the  latter  element 
was  taken  as  4-6.  Great  advances  in  this  subject  were  then 
made  by  the  Swedish  chemist  Berzelius.  For  fixing  the  pro- 
portional numbers,  he  depended  to  some  extent,  like  Dalton, 
on  the  assumption  of  simplicity  of  composition,  but  was  able 
to  check  the  numbers  thus  obtained  by  the  application  of  Gay- 
Lussac's  law  of  volumes  and  Dulong  and  Petit's  law.  Later 
still,  the  discovery  of  isomorphism  by  Mitscherlich  afforded  yet 
another  means  of  checking  the  atomic  weights.  Besides  these 
physical  methods,  chemical  methods  may  also  be  used  for  fixing 
the  atomic  weights  of  the  elements.  Each  of  these  methods 
will  now  be  shortly  referred  to. 

(a)  Volumetric  Method.  Gay-Lussac's  Law  of  Volumes. 
Avogadro's  Hypothesis — Gay-Lussac,  on  the  basis  of  an 
extensive  series  of  experiments  on  the  combining  volumes  of 
gases,  established  'the  law  of  gaseous  volumes,  which  may  be 
expressed  as  follows  : — 

Gases  combine  in  simple  ratios  by  volume^  and  the  volume  oj 
the  gaseous  product  bears  a  simple  ratio  to  the  volumes  of  the  re- 
acting gases ',  when  measured  under  the  same  conditions. 

A  few  years  before,  the  same  chemist  had  discovered  that 
all  gases  behave  similarly  with  regard  to  changes  of  pressure 
and  temperature,  and  this  fact,  taken  in  conjunction  with  the 
law  of  volumes  and  the  atomic  theory,  seemed  to  point  to  some 
simple  relation  between  the  number  of  particles  in  equal  volumes 
of  different  gases.  Berzelius  suggested  that  equal  volumes  of 
different  gases,  under  corresponding  conditions  of  temperature 
and  pressure,  contain  the  same  number  of  atoms.  It  was  soon 
found,  however,  that  this  assumption  was  untenable,  and  the 


ro         OUTLINES  OF  PHYSICAL  CHEMISTRY 

view  held  at  the  present  day  was  first  enunciated  by  the  Italian 
physicist  Avogadro.  He  drew  a  distinction  between  atoms,  the 
smallest  particles  which  can  take  part  in  chemical  changes,  and 
molecules,  the  smallest  particles  which  can  exist  in  a  free  con- 
dition, and  expressed  his  hypothesis  as  follows  : — 

Equal  volumes  of  all  gases,  under  the  same  conditions  oj 
temperature  and  pressure,  contain  the  same  number  of  molecules. 

In  expressing  the  results  of  determinations  of  the  densities 
of  different  gases,  hydrogen,  as  the  lightest  gas,  is  taken  as 
standard,  and  the  number  expressing  the  ratio  of  the  weights 
of  equal  volumes  of  another  gas  (or  vapour)  and  hydrogen, 
measured  under  the  same  conditions,  is  the  density  of  the  gas 
(or  vapour  density  in  the  case  of  a  vapour).  From  Avogadro's 
hypothesis  it  follows  at  once  that  the  ratio  of  the  vapour  densities 
of  another  gas  and  hydrogen,  being  a  comparison  of  the  relative 
weights  of  an  equal  number  of  molecules,  is  also  the  ratio  of  the 
molecular  weights.  It  is  usual  to  refer  both  atomic  and  mole- 
cular weights  to  the  atom  of  hydrogen  as  unity,1  and  therefore  the 
molecular  weight,  being  referred  to  a  standard  half  that  to  which 
the  vapour  density  is  referred,  is  double  the  vapour  density. 

When  the  molecular  weight  is  known,  it  is  a  comparatively 
simple  matter  to  establish  the  atomic  weight.  As  an  example, 
we  may  employ  the  volumetric  method  to  fix  the  atomic  weight 
of  beryllium,  a  matter  of  great  historical  interest.  It  was  found 
by  analysis  that  beryllium  chloride  contains  4*55  parts  of  beryllium 
to  3 5 '5  parts  of  chlorine  by  weight;  in  other  words,  the  chemi- 
cal equivalent  of  beryllium  is  4-55.  If  beryllium  be  regarded  as 
a  bivalent  metal  (p.  1 6),  the  formula  for  the  chloride  will  be  BeQ2, 
and  its  atomic  weight  2  x  4-55  =  9-1.  If,  however,  it  is  trivalent, 
the  formula  for  the  chloride  must  be  BeCl3,  and,  to  obtain  the 
ratio  for  Be  :  Cl  found  experimentally,  its  atomic  weight  must  be 
4*55  x  3  =  I3'^5.  The  vapour  density  of  the  chloride  was  de- 
termined by  Nilson  and  Petterson,  and  from  the  result  the  mole- 
cular weight  calculated  as  80*1.  The  molecule  of  beryllium 

1  Strictly  speaking,  to  the  atom  of  oxygen  as  16  (p.  18). 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     n 

chloride  cannot  therefore  contain  more  than  35*5  x  2  =  71  parts 
of  chlorine,  the  formula  for  the  chloride  is  BeCl2,  and  the  atomic 
weight  of  beryllium  9*1. 

The  determination  of  atomic  weights  by  the  volumetric 
method  thus  reduces  to  finding  the  smallest  quantity  of  an 
element  present  in  a  molecule ,  referred  to  the  atom  of  hydrogen 
as  unity.  If  the  molecular  weights  of  a  large  number  of  vola- 
tile compounds  containing  a  particular  element  are  determined, 
it  is  practically  certain  that  at  least  some  of  the  compounds  will 
contain  only  one  atom  of  the  element  in  question,  and  the  pro- 
portion in  which  the  element  is  present  in  these  compounds  is 
its  atomic  weight.  In  the  above  example,  for  instance,  it  has 
been  assumed  that  only  one  atom  of  beryllium  is  present  in 
the  molecule  of  beryllium  chloride  of  weight  8o'i,  and  the 
justification  for  this  assumption  is  that  no  compound  is 
known  the  molecule  of  which  contains  less  than  9*1  parts  of 
beryllium.  It  is  clear  that  the  numbers  thus  obtained  are 
maximum  values,  and  the  possibility  is  not  excluded  that  the 
true  values  may  be  fractions  of  those  thus  arrived  at.  The 
values  generally  accepted  are,  however,  confirmed  by  so  many 
independent  methods  that  every  confidence  can  be  placed  in 
their  trustworthiness. 

(b)  Dulong  and  Petit's  Law — In  1818,  the  French  chemists 
Dulong  and  Petit  enunciated  the  important  kw  that  for  solid 
elements  the  product  of  the  specific  heat  and  atomic  weight  is 
constant^  amounting  to  about  6*4.  This  law  is  a  very  striking 
one  when  the  great  differences  in  the  magnitude  of  the  atomic 
weights  are  taken  into  account.  Thus,  the  specific  heat  of  lead 
— the  ratio  of  the  quantity  of  heat  required  to  raise  i  gram 
of  the  metal  i°  in  temperature  to  that  required  to  raise  the 
temperature  of  the  same  weight  of  water  i° — is  0*031,  and  its 
atomic  weight  207,  the  product  being  6-4;  whilst  for  lithium, 
with  a  specific  heat  of  0*9  and  an  atomic  weight  of  7,  the 
product  is  6*3.  Since  quantities  of  the  different  elements  in 
the  proportion  of  their  atomic  weights  require  the  same  amount 


12         OUTLINES  OF  PHYSICAL  CHEMISTRY 


of  heat  to  raise  the  temperature  by  a  definite  number  of  degrees, 
the  law  may  also  be  expressed  as  follows  :  The  atoms  of  all  ele- 
ments have  the  same  capacity  for  heat. 

It  is  clear  that  this  law  can  be  used  to  determine  the  atomic 
weight  of  an  element  when  the  specific  heat  is  known,  the 
quotient  of  the  constant  by  the  specific  heat  giving  the  re- 
quired value.  Dulong  and  Petit's  law  was  largely  used  by 
Berzelius  in  fixing  the  values  of  the  atomic  weights. 

Like  many  other  empirical  laws,  that  of  Dulong  and  Petit  is 
only  approximately  true,  the  "  constant  "  varying  from  about 
6*0  to  67.  This  degree  of  concordance  is,  of  course,  quite 
sufficient  for  fixing  the  values  of  the  atomic  weights,  as  it  is 
only  necessary  for  this  purpose  to  choose  between  a  number 
and  a  simple  multiple  or  submultiple.  Moreover,  the  specific 
heat  varies  with  the  allotropic  form  of  the  element  and  with  the 
temperature,  and  there  is  much  uncertainty  as  regards  the  proper 
conditions  for  comparison.  Regnault,  who  made  a  series  of 
very  careful  determinations  of  specific  heats,  showed  that  most 
elements  of  small  atomic  weight,  more  particularly  carbon,  silicon 
and  boron,  have  exceptionally  small  atomic  heats.  Later,  how- 
ever, it  was  found  that  the  specific  heats  of  these  elements 
increase  rapidly  with  rise  of  temperature,  and  at  high  tempera- 
tures their  behaviour  is  in  approximate  accordance  with  Dulong 
and  Petit's  law.  This  is  clear  from  the  accompanying  table, 
showing  the  behaviour  of  carbon  (diamond)  and  boron. 


CARBON  (DIAMOND). 

BORON. 

Temp. 

Sp.  Heat. 

Atomic  Heat. 

Temp. 

Sp.  Heat. 

Atomic  Heat. 

10° 

206° 
600° 

1000° 

0-1128 
0-2733 
0*4408 
0-4589 

l'33 
3'25 

5-28 
5-51 

27° 
126° 
177° 
233° 

0-2382 
0-3069 
0-3378 
0-3663 

2'6l 
3H° 
370 
4-02 

The  few  elements  which  show  this  abnormal  behaviour  are  of 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     13 

low  atomic  weight,  but  the  converse    does   not  hold,  as  the 
atomic  heat  of  lithium  is  normal. 

Some  years  after  the  introduction  of  Dulong  and  Petit's  law, 
a  similar  law  for  compounds  was  enunciated  by  Neumann.  He 
showed  that,  for  compounds  of  similar  chemical  character,  the 
product  of  specific  heat  and  molecular  weight  is  constant — in 
other  words,  the  molecular  heats  of  similarly  constituted  com- 
pounds in  the  solid  state  are  equal.  In  1864,  Kopp  extended 
Neumann's  law  by  showing  that  the  molecular  heat  of  solid 
compounds  is  an  additive  property,  being  made  up  of  the 
sum  of  the  atomic  heats  of  the  component  atoms.  It  follows 
that  in  certain  cases  atoms  have  the  same  capacity  for  heat 
before  and  after  entering  into  chemical  combination.  For  ex- 
ample, the  specific  heat  of  calcium  chloride  is  0*174,  the  mole- 
cular heat  is  therefore  0-174  x  in  =  19-3,  and  the  atomic  heat 
of  each  atom  6-4. 

This  law  may  be  used  to  estimate  the  atomic  heats  of  sub- 
stances which  cannot  be  readily  investigated  in  the  solid  form. 
The  atomic  heat  of  solid  oxygen  in  combination  is  about  4*0, 
and  of  solid  hydrogen  2*3. 

(c)  Isomorphism — Mitscherlich  observed  that  the  corre- 
sponding salts  of  arsenic  acid,  H3AsO4,  and  phosphoric  acid, 
H3PO4,  crystallize  with  the  same  number  of  molecules  of  water, 
are  identical,  or  nearly  so,  in  crystalline  form,  and  can  be  obtained 
from  mixed  solutions  in  crystals  containing  both  salts,  so-called 
mixed  crystals.  On  the  basis  of  these  and  similar  observations, 
Mitscherlich  established  the  Law  of  Isomorphism,  according  to 
which  compounds  of  the  same  crystalline  form  are  of  analogous 
constitution.  Thus,  when  one  element  replaces  another  in  a 
compound  without  altering  the  crystalline  form,  it  is  assumed 
that  one  element  has  displaced  the  other  atom  for  atom.  The 
replacing  quantities  of  the  different  elements  are  therefore  in 
the  ratio  of  their  atomic  weights,  and  if  the  atomic  weight  of 
one  of  them  is  known,  that  of  the  other  can  be  calculated. 
This  principle  was  largely  used  by  Berzelius  for  fixing  atomic 


i4          OUTLINES  OF  PHYSICAL  CHEMISTRY 

weights  before  the  establishment  of  Dulong  and  Petit's  law,  and 
afforded  a  welcome  corroboration  of  those  obtained  by  the  use 
of  the  law  of  volumes.  The  converse  to  the  law  of  isomorphism 
does  not  hold,  as  elements  may  displace  one  another  atom  for 
atom  with  complete  alteration  of  crystalline  form. 

The  principle  of  isomorphism  is,  however,  somewhat  in- 
definite, inasmuch  as  even  the  most  closely  related  compounds 
are  not  completely  identical  in  crystalline  form,  and  it  is 
difficult  to  decide  where  the  line  between  similarity  and  want 
of  similarity  is  to  be  drawn.  Thus  the  corresponding  angles 
for  the  naturally-occurring  crystals  of  the  carbonates  of  cal- 
cium, strontium  and  barium  are:  Aragonite,  116°  10';  Stron- 
tianite,  117°  19';  Witherite,  118°  30'.  Tutton,1  from  a  careful 
comparative  study  of  the  sulphates  and  selenates  of  potassium, 
rubidium  and  caesium,  has  shown  that  each  salt  has  its  own 
specific  interfacial  angle,  but  the  differences  produced  by  dis- 
placing one  metal  of  the  alkali  series  by  another  does  not  exceed 
i°  of  arc,  and  is  usually  much  less.  The  three  most  important 
characteristics  for  the  establishment  of  isomorphism  are : — 

(1)  The  capacity  of  forming  mixed  crystals.      The  miscibility 
must  be  complete,  or  within  fairly  wide  limits  of  concentration. 

(2)  Similarity  of  crystalline  form,  which  must  include  at  least 
approximate  agreement  in  the  values  of  the  geometrical  con- 
stants. 

(3)  The  capacity  of  crystals  of  one  substance  to  increase  in 
size  in  a  saturated  solution  of  the  other. 

(d)  Determination  of  Atomic  Weights  by  Chemical 
Methods — It  is  evident  from  the  considerations  advanced  in 
the  section  on  the  determination  of  atomic  weights  by  volu- 
metric methods  (p.  10)  that  if  the  composition  of  a  binary 
compound  containing  one  or  more  atoms  of  an  element  such  as 
hydrogen  or  chlorine  for  each  atom  of  an  element  of  unknown 
atomic  weight  has  been  determined  by  analysis,  and  if  further 
the  relative  number  of  atoms  of  hydrogen  or  chlorine  present  is 

1  Science  Progress,  1906,  I,  p.  91. 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     15 

known,  the  atomic  weight  of  the  other  element  can  at  once  be 
calculated.  In  the  case  of  beryllium  chloride,  it  has  been 
shown  that  the  number  of  chlorine  atoms  present  can  be  deter- 
mined by  a  physical  method  (p.  10),  but  such  determinations 
can  sometimes  be  made  by  purely  chemical  methods.  As  an 
illustration,  we  will  consider  the  determination  of  the  atomic 
weight  of  oxygen.  Analysis  shows  that  water  contains  approxi- 
mately i  part  of  hydrogen  to  8  parts  of  oxygen  by  weight.  If 
the  molecule  of  water  contains  one  atom  each  of  hydrogen  and 
oxygen,  its  formula  must  be  HO  and  the  atomic  weight  of 
oxygen  will  be  8  ;  if,  on  the  other  hand,  two  atoms  of  hydrogen 
are  present,  the  formula  must  be  H2O  and  the  atomic  weight  of 
oxygen  must  be  16  in  order  to  obtain  the  ratio  between  the 
weights  of  the  elements  found  experimentally.  It  has  been 
found  that  by  the  action  of  metallic  sodium  half  the  hydrogen 
in  water  can  be  displaced,  and  as  by  definition  atoms  are  indi- 
visible, this  indicates  that  the  molecule  of  water  contains  two  (or 
a  multiple  of  two)  atoms  of  hydrogen.  The  (probable)  formula 
for  water  is  therefore  H2O  and  the  atomic  weight  of  oxygen  16. 

It  will  be  evident  that,  as  in  the  case  of  the  volumetric 
method,  the  value  thus  obtained  for  the  atomic  weight  is  a 
maximum  and  further  experiments  are  necessary  to  fix  the 
value  definitely. 

Relation  between  Atomic  Weights  and  Chemical 
Equivalents.  Valency — The  exact  proportions  in  which 
the  elements  enter  into  chemical  combination  are  determined 
by  analysis,  and  the  numbers  thus  obtained,  referred  to  a 
definite  standard,  represent,  according  to  the  atomic  theory,  the 
atomic  weights,  or  simple  multiples  or  sub-multiples  of  the 
atomic  weights,  of  the  respective  elements.  The  choice  between 
several  possible  numbers  is  based  on  the  methods  discussed  in 
the  foregoing  paragraphs,  more  particularly  on  Avogadro's  hypo- 
thesis, and  the  fact  that  these  independent  methods  give  the 
same  values  affords  strong  evidence  that  the  numbers  thus  ob- 
tained are  the  true  ones — a  view  which  obtains  still  further 


16         OUTLINES  OF  PHYSICAL  CHEMISTRY 

support  from  the  periodic  classification  of  the  elements  due  to 
Mendeleeff  (1869). 

The  ordinary  chemical  formulae  with  which  the  student  is 
familiar  are  based  on  the  atomic  weights  thus  obtained.  For 
example,  the  formulae  of  a  number  of  compounds  containing 
only  hydrogen  and  one  other  element  are  as  follows :  HC1, 
H2O,  NH3,  CH4.  It  is  evident  from  these  formulae  that  the 
power  of  different  elements  to  combine  with  hydrogen  is  very 
different ;  whilst  one  atom  of  chlorine  combines  with  only  one 
atom  of  hydrogen,  one  atom  of  carbon  can  become  associated 
with  no  less  than  four  atoms  of  hydrogen.  The  combining 
capacity  of  an  element  for  hydrogen  or  other  univalent  element 
is  termed  the  valency  of  an  element,  chlorine  being  a  univalent 
and  carbon  a  quadrivalent  element.  A  little  consideration  of 
the  above  formulae  will  make  clear  the  relationship  between  the 
atomic  weight  and  the  chemical  equivalent  of  an  element.  It 
is  clear  that  an  amount  of  one  element  equivalent  to  its  atomic 
weight  may  combine  with  (or  displace)  i,  2,  3  or  more  parts 
of  hydrogen  by  weight,  depending  on  its  valency.  Since  the 
chemical  equivalent  of  an  element  is  that  amount  of  it  which 
can  combine  with  or  displace  ont  part  by  weight  of  hydrogen  it 
follows  that 

Atomic  weight  _  chemical        ivalent 
Valency 

As  has  been  indicated  in  the  foregoing  paragraphs,  the 
atomic  weight  and  the  chemical  equivalent  are  often  deter- 
mined more  or  less  independently  and  the  quotient  of  the  two 
values  is  the  valency.  In  other  cases,  however  (for  example, 
the  volumetric  method  and  the  chemical  method),  the  chemical 
equivalent  and  the  valency  are  determined,  and  the  product  of 
the  two  is  the  atomic  weight. 

The  Values  of  the  Atomic  Weights — After  the  establish- 
ment of  the  law  of  multiple  proportions  and  the  formulation  of 
the  atomic  theory  by  Dalton,  it  became  a  matter  of  the  utmost 
importance  for  chemists  to  determine  the  atomic  weights  of 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     17 

the  elements  with  the  greatest  possible  accuracy.  This  task 
was  undertaken  by  Berzelius,  who,  in  the  course  of  about  six 
years  (1810-1816),  fixed  the  combining  weights  of  most  of 
the  known  elements.  Since  then,  the  determination  of  atomic 
weights  has  proceeded  regularly,  but  on  two  occasions  a 
special  impulse  was  given  to  these  investigations.  The  first 
occasion  was  a  suggestion  by  Prout  that  the  atomic  weights 
are  exact  multiples  of  that  of  hydrogen.  The  idea  under- 
lying this  assertion  was  that  hydrogen  is  the  primary  element, 
the  other  elements  being  formed  from  it  by  condensation. 
The  results  of  Berzelius  were  incompatible  with  Prout's 
hypothesis,  but  as  the  atomic  weights  of  certain  elements  un- 
doubtedly approximated  to  whole  numbers,  Stas  made  a  number 
of  atomic  weight  determinations  with  a  degree  of  accuracy  which 
has  only  been  improved  upon  in  quite  recent  times.  The  results 
obtained  by  Stas  completely  disposed  of  Prout's  hypothesis  in 
its  original  form. 

The  second  event  which  stimulated  atomic  weight  investiga- 
tions was  the  development  of  the  periodic  classification  of  the 
elements.  In  certain  cases,  the  order  of  the  elements,  arranged 
according  to  their  atomic  weights,  did  not  correspond  with  their 
chemical  behaviour,  and  Mendeleeff  asserted  that  in  these 
cases  the  commonly  accepted  atomic  weights  were  inaccurate. 
The  investigations  undertaken  to  test  these  suggestions  afforded 
striking  confirmation  of  MendeleefPs  views  in  some  cases,  but 
not  in  others.  As  regards  recent  progress  in  this  branch  of 
investigation  special  mention  should  be  made  of  the  determina- 
tion of  the  combining  ratios  of  hydrogen  and  oxygen  by  Morley l 
and  of  the  comprehensive  and  masterly  investigations  of  T.  W. 
Richards  and  his  co-workers.2 

As  the  combining  weights  are  relative,  it  is  necessary  to  fix 
on  a  standard  to  which  they  may  be  referred.  Dalton  took  the 
atomic  weight  of  hydrogen,  the  lightest  element,  as  unit,  but 

1  Smithsonian  Contributions  to  Knowledge,  1895. 

2  See,  for  example,  J.Amer.  Chem.  Soc.,  1907,  29,  808-826. 
2 


1 8          OUTLINES  OF  PHYSICAL  CHEMISTRY 

Berzelius,  from  practical  considerations,  proposed  oxygen  as 
standard,  putting  its  atomic  weight  =  100.  The  justification 
for  this  procedure  is  that  very  few  elements  form  compounds 
with  hydrogen  suitable  for  analysis  ;  the  majority  of  determina- 
tions have  been  made  with  compounds  containing  oxygen,  and 
until  comparatively  recently  the  ratio  of  the  atomic  weights  of 
hydrogen  and  oxygen  was  not  accurately  known.  Although 
the  hydrogen  standard  again  came  into  use  after  the  time  of 
Berzelius,  mainly  because  hydrogen  was  taken  as  a  standard  for 
other  properties,  yet  in  more  recent  times  the  oxygen  standard 
has  again  come  most  largely  into  use,  the  atomic  weight  of  that 
element  being  taken  as  i6'oo.  The  unit  to  which  atomic 
weights  are  referred  is  therefore  ^  of  the  atomic  weight  of 
oxygen,  and  is  rather  less  than  the  atomic  weight  of  hydrogen.1 
Besides  the  advantage  already  mentioned,  the  atomic  weights  of 
more  of  the  elements  approximate  to  whole  numbers  when  the 
oxygen  standard  is  used,  which  is  a  distinct  advantage,  since 
round  numbers  are  generally  used  in  calculations. 

Chemical  equivalents,  like  atomic  weights,  should  be  referred 
to  the  oxygen  standard,  and  the  chemical  equivalent  of  an 
element  is  a  number  representing  that  quantity  of  it  which 
combines  with,  or  displaces,  8  parts  by  weight  of  oxygen. 

The  arguments  in  favour  of  the  oxygen  standard  seem  con- 
clusive, and  as  it  is  very  confusing  to  have  two  standards  in 
general  use,  it  is  very  satisfactory  that  the  International  Com- 
mittee on  Atomic  Weights  now  use  the  oxygen  standard  only. 

1  According  to  the  recent  determinations  of  Morley,  Rayleigh  and  others 
the  atomic  weight  of  oxygen  is  about  15*88  when  hydrogen  is  taken  as 
unit.  It  follows  that  on  the  oxygen  standard,  O  =  16-00,  the  atomic  weighf. 
of  hydrogen  is  about  i'oo8. 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     19 
INTERNATIONAL  ATOMIC  WEIGHTS  (1912) 


Elements. 

Sym- 
bols. 

At.  Wt. 
O  =  i6. 

Elements. 

Sym- 
bols. 

At.  Wt. 

O  =  16. 

Aluminium 

Al 

27-1 

Neodymium 

Nd 

I44'3 

Antimony  . 

Sb 

I20'2 

Neon 

Ne 

20'2 

Argon 

A 

39-88 

Nickel 

Ni 

58-68 

Arsenic 

As 

74-96 

Niton 

Barium 

Ba 

i37'37 

(Radium  Emana- 

Bismuth     .         . 

Bi 

208-0 

tion) 

Nt 

222'4 

Boron          . 

B 

ii-o 

Nitrogen     . 

N 

14-01 

Bromine     . 

Br 

79-92 

Osmium 

Os 

190-9 

Cadmium    . 

Cd 

112-40 

Oxygen 

O 

16-00 

Caesium     . 

Cs 

132-81 

Palladium  . 

Pd 

106-7 

Calcium 

Ca 

40-07 

Phosphorus 

P 

31-04 

Carbon 

C 

I2'OO 

Platinum 

Pt 

195-2 

Cerium 

Ce 

140-25 

Potassium  . 

K 

39-10 

Chlorine     . 

Cl 

35H6 

Praseodymium    . 

Pr 

140-6 

Chromium  . 

Cr 

52-0 

Radium 

Rd 

226-4 

Cobalt 

Co 

58'97 

Rhodium     . 

Rh 

1  02  '9 

Columbium 

Cb 

93-5 

Rubidium   . 

Rb 

85-45 

Copper 

Cu 

63-57 

Ruthenium 

Ru 

1017 

Dysprosium 

Dy 

162-5 

Samarium  . 

Sa 

150-4 

Erbium 

Er 

167-7 

Scandium  . 

Sc 

44-1 

Fluorine     . 

F 

19-0 

Selenium    . 

Se 

792 

Gadolinium 

Gd 

J57'3 

Silicon 

Si 

28-3 

Gallium 

Ga 

69-9 

Silver. 

Ag 

107-88 

Germanium 

Ge 

72*5 

Sodium       .         . 

Na 

23-00 

Glucinum  . 

Strontium  . 

Sr 

87-63 

(beryllium) 

Gl 

9-1 

Sulphur 

S 

32-07 

Gold  .         .         . 

Au 

197-2 

Tantalum  . 

Ta 

181-5 

Helium 

He 

3*99 

Tellurium  . 

Te 

127-5 

Hydrogen  . 

H 

I'ooS 

Terbium 

Tb 

159-2 

Indium 

In 

114-8 

Thallium    . 

Tl 

204-0 

Iodine 

I 

126-92 

Thorium     . 

Th 

232-4 

Iridium 

Ir 

193-1 

Thulium     . 

Tm 

168-5 

Iron    . 

Fe 

55^4 

Tin     . 

Sn 

119-0 

Krypton 

Kr 

82-9 

Titanium    . 

Ti 

48-1 

Lanthanum 

La 

139-0 

Tungsten    . 

W 

184-0 

Lead  . 

Pb 

207-10 

Uranium     . 

U 

238-5 

Lithium 

Li 

6-94 

Vanadium  . 

V 

51-0 

Lutecium    . 

Lu 

174-0 

Xenon 

Xe 

130-2 

Magnesium 

Mg 

24-32 

Ytterbium 

Manganese 

Mn 

54*93 

(Neoytterbium). 

Yb 

172-0 

Mercury 
Molybdenum 

Hg 
Mo 

200-6 
96*0 

Yttrium 
Zinc    . 

Yt 
Zn 

89-0 
OS'S? 

Zirconium  . 

Zr 

90-6 

Only  significant  figures  are  given  in  the  table.  Where  no 
figure  follows  the  decimal  point,  the  value  of  the  first  decimal 
is  uncertain. 


20         OUTLINES  OF  PHYSICAL  CHEMISTRY 

The  Periodic  System — It  was  early  observed  that  there 
are  some  remarkable  relationships  between  the  magnitude  of 
the  atomic  weights  of  the  elements  and  their  chemical  behaviour. 
The  most  important  observation  in  this  connection  is  that  the 
differences  in  the  atomic  weights  of  successive  members  of  the 
same  group  of  elements  are  approximately  16  or  a  multiple  of 
that  number.  Thus  for  the  halogen  group,  F  =  19,  Cl  =  35*5, 
Br  =  80,  I  =  127,  the  differences  between  each  element  and 
its  immediate  predecessor  are  16*5,  44*5  and  47  respectively, 
the  latter  two  numbers  being  approximately  3x16.  Further, 
for  the  members  of  the  alkali  group,  Li  =  7,  Na  =  23,  K  =  39, 
Rb  =  85*5,  Cs  =  132*9,  the  differences  are  16,  16,  46-5  and 
47*2  respectively. 

In  1864,  a  considerable  advance  was  made  by  the  English 
chemist  Newlands,  which  is  summarised  in  the  law  of  octaves. 
He  pointed  out  that  when  the  elements,  beginning  with  lithium, 
are  arranged  in  the  order  of  ascending  atomic  weights,  there  is 
a  gradual  variation  in  properties  till  the  eighth  element  is 
reached  ;  this  element  (sodium)  shows  a  strong  resemblance  to 
the  first  element,  lithium,  the  ninth  element,  magnesium,  is 
similar  in  chemical  behaviour  to  beryllium,  and  so  on.  The 
first  fourteen  elements  may  therefore  be  arranged  as  follows : — 

Li=7     Be  =  9        B  =  n    C=i2    N=i4   O=i6    F=i9 
Na=23    Mg=24    Al=27    Si  =  2.8    P  =  3i    8  =  32    Cl  =  35'5 

and  the  elements  which  show  similar  chemical  behaviour  are 
thus  brought  into  the  same  vertical  row.  On  these  lines,  but 
without  any  knowledge  of  the  views  of  Newlands,  a  complete 
system  for  classifying  the  elements,  termed  the  periodic  system 
was  later  developed  by  Mendeleeff.  The  system  is  based  on 
the  observation  that  when  the  elements  are  arranged  in  the 
order  of  ascending  atomic  weights,  elements  with  similar  chemical 
properties  recur  at  regular  intervals. 


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22          OUTLINES  OF  PHYSICAL  CHEMISTRY 

The  accompanying  table  (p.  21),  in  which  the  atomic  weights 
are  only  approximate,  is  practically  the  same  as  that  proposed 
originally  by  Mendeleeff.  Starting  with  helium  =  4  (which 
was  unknown  in  Newlands'  time)  we  have  the  arrangement 
shown  in  the  first  line  of  the  table,  in  which  the  properties 
vary  regularly  from  the  first  member  to  fluorine.  The  next 
element,  neon  =*=  20,  is  an  inactive  gas,  and  is  therefore  placed 
below  helium,  sodium  falls  into  its  proper  place  below  lithium, 
and  so  on.  The  first  and  second  periods  possess  8  elements 
each.  A  third  period  is  started  with  potassium,  but  in  this  case 
it  is  necessary  to  pass  over  18  elements  before  another  metal 
(rubidium),  bearing  a  close  resemblance  to  potassium,  is  reached. 
Such  a  period  of  18  elements  is  termed  a  long  periodic,  contrast 
to  the  two  short  periods  of  8  elements  each.  The  whole  table 
is  made  up  of  two  short  and  five  long  periods,  but  four  of  the 
long  periods  are  incomplete  and  the  last  one  contains  only 
three  elements.  The  positions  of  the  elements  in  these  periods 
are  fixed  by  their  chemical  relationships  with  those  above  them 
(in  the  vertical  rows),  and  it  is  assumed  that  the  blanks  indicate 
the  positions  of  elements  which  have  not  yet  been  discovered. 
The  arrangement  of  the  three  intermediate  elements  in  each  of 
the  first  three  long  periods  presented  a  certain  difficulty,  and 
Mendeleeff  put  them  in  a  group  by  themselves,  the  so-called 
eighth  group  (group  vm.  in  the  table). 

A  study  of  the  elements  arranged  as  above  reveals  many 
striking  regularities.  Thus  the  valency  with  regard  to  hydrogen 
increases  regularly  up  to  the  middle  of  a  short  period  and  then 
falls  to  unity,  whilst  the  valency  for  oxygen  increases  regularly 
from  the  beginning  to  the  end  of  a  period.  Helium  and  the 
elements  in  the  same  vertical  row  do  not  enter  into  chemical 
combination,  and  may  therefore  be  regarded  as  having  zero 
valency.  The  valency  relations  in  the  long  periods  are  not 
quite  so  regular,  being  complicated  by  the  fact  that  most  of 
the  elements  have  several  valencies. 

Many  of  the  physical  properties  of  the  elements,  such  as  the 


FUNDAMENTAL  PRINCIPLES  OF  CHEMISTRY     23 

melting-point,  the  atomic  volume  and  the  density,  also  vary 
regularly  within  each  period.  For  example,  the  melting-points 
in  the  first  series  gradually  rise  from  helium  to  carbon  and  fall 
again  to  fluorine,  and  similarly  the  elements  of  highest  melting- 
point  (iron,  cobalt,  nickel,  etc.)  occur  in  the  middle  of  the 
long  periods.  Besides  this  variation  of  physical  properties  in 
the  horizontal  series,  there  is  a  similar,  but  much  less  marked, 
variation  in  the  vertical  series ;  in  the  case  of  the  alkali  metals, 
for  example,  there  is  a  gradual  fall  in  the  melting-point  from 
lithium  to  caesium. 

Not  only  the  physical  properties,  but  also  the  chemical 
properties  of  the  elements  vary  regularly  within  the  periods. 
Thus  the  elements  on  the  extreme  left  hand  of  the  table  are 
inactive  gases,  those  in  the  second  group  decompose  water  and 
are  strongly  electropositive,  at  the  middle  of  the  period  they 
appear  to  be  electrically  indifferent  (carbon,  silicon)  and  towards 
the  right  hand  strongly  electronegative. 

The  statements  in  the  last  three  paragraphs  are  summarised 
in  the  periodic  law,  due  to  Mendeleeff,  which  may  be  expressed 
as  follows :  The  properties  of  the  elements,  as  well  as  the  proper- 
ties of  their  compounds^  are  periodic  functions  of  the  atomic 
weights. 

The  arrangement  of  the  elements  according  to  the  periodic 
system  is  not  in  all  respects  satisfactory.  Copper,  silver  and 
gold  do  not  fit  very  well  into  their  positions  beside  the  alkali 
metals,  and  it  has  been  suggested  that  they  belong  more 
properly  to  the  eighth  group,  coming  after  nickel,  palladium 
and  platinum  respectively.  Further,  the  atomic  weight  of  argon 
is  greater  than  that  of  potassium,  but  the  former  element  must 
undoubtedly  precede  the  latter  in  the  periodic  table.  The 
question  which  has  raised  most  discussion  in  this  connection, 
however,  is  the  relative  position  of  tellurium  and  iodine. 
Although  from  its  chemical  relationships  the  latter  element 
must  follow  tellurium,  yet  experiment  shows  that  the  atomic 
weight  of  tellurium  is  greater  than  that  of  iodine.  It  is  at  first 


24          OUTLINES  OF  PHYSICAL  CHEMISTRY 

natural  to  suppose  that  there  must  have  been  some  mistake  in 
determining  the  atomic  weights,  but  the  recent  work  of  Laden - 
burg,  Puccini,  Kothner,  Brereton  Baker1  and  others  leave 
practically  no  room  for  doubt  that  the  facts  are  as  stated.  It  is 
unquestionable  that  the  periodic  system  is  of  great  value,  but 
the  above  considerations  indicate  that  it  is  only  a  first  approxi- 
mation to  a  satisfactory  system. 

The  periodic  system  is  of  use  mainly  in  three  ways  : — 

(a)  As  a  system  of  classification  which  indicates  in  a  fairly 
satisfactory  way  the  chemical  and  physical  relationships  of  the 
elements. 

(b)  For  predicting  the   existence  and  properties  of  elements 
hitherto  undiscovered. 

(c)  For  enabling  us  to  fix  the  correct  values  of  the  atomic 
weights  of  elements  which  do  not  form  volatile  compounds. 

When  the  periodic  system  was  first  brought  forward,  there 
were  more  blanks  in  the  table  than  there  are  at  the  present  day, 
and  Mendeleeff  not  only  suggested  that  the  positions  of  these 
blanks  corresponded  with  hitherto  undiscovered  elements,  but 
even  foretold  the  properties  of  the  missing  members  of  the 
series  from  the  known  properties  of  the  elements  near  them  in 
the  periodic  table.  It  is  an  interesting  historical  fact  that 
within  a  few  years  three  of  the  blanks  had  been  filled  by  ele- 
ments— gallium  (1875),  scandium  (1879),  germanium  (1886) — 
having  in  all  respects  the  properties  foretold  by  Mendeleeff. 

The  use  of  the  periodic  system  for  fixing  atomic  weights  will 
be  readily  understood  from  the  foregoing.  When  the  equivalent 
of  the  element  has  been  determined,  it  is  usually  possible  to 
decide  which  multiple  of  it  is  to  be  taken,  as  there  will  in 
general  be  only  one  position  in  the  table  into  which  the  element 
can  be  satisfactorily  fitted. 

1  Trans.  Chem.  Soc.,  1907,  91,  1849. 


CHAPTER  II 
GASES 

The  Gas  Laws — The  gaseous  form  of  matter  is  charac- 
terised by  its  tendency  to  fill  completely  and  to  a  uniform 
density  any  available  space.  In  general,  gases  are  less  dense 
than  other  forms  of  matter,  and  their  internal  friction  is 
much  less.  In  consequence  of  this,  the  laws  expressing  the 
behaviour  of  gases  under  varying  conditions  are  much  simpler 
than  those  holding  for  liquids  and  solids.  The  most  striking 
fact  about  these  laws  is  that  they  are  to  a  great  extent  inde- 
pendent of  the  nature  of  the  gas  :  the  volume  of  all  gases  is 
affected  by  changes  of  temperature  and  pressure  to  much  the 
same  extent. 

The  well-known  laws  which  represent  more  or  less  accurately 
the  behaviour  of  all  gases  under  varying  conditions  may  be 
enunciated  as  follows  : — 

1.  At  constant  temperature,  the  volume ,  v,  of  a  given  mass  of 
any  gas  is  inversely  proportional  to  the  pressure^  p  ',   otherwise 
expressed,  pv  =  constant  (Boyle,  1662). 

2.  At  constant  pressure,  the  volume,  v,  of  a  given   mass  of 
any  gas  is  proportional  to  its  absolute  temperature,  T  (273°  + 
temp.  Centigrade]  (Gay-Lussac,  1802). 

3.  At  constant  volume,  the  pressure  of  a  given  mass  of  any 
gas  is  proportional  to  its  absolute  temperature. 

These  laws  are  not  independent ;  when  any  two  of  them  are 
known,  the  third  can  readily  be  deduced. 

The  three  laws  just  given  may  be  summarised  in  a  single 


26          OUTLINES  OF  PHYSICAL  CHEMISTRY 

equation,  which  represents  the  behaviour  of  a  gas  when  any  two 
of  the  determining  factors  are  varied.  Let  /0,  v0  and  T0  repre- 
sent the  original  pressure,  volume  and  temperature  of  a  definite 
quantity  of  a  gas,  and  plt  v^  and  Tl  the  final  values.  Suppose 
that  at  first  the  pressure  is  altered  from  pQ  to  its  final  value  p^ 
at  constant  temperature,  then,  by  Boyle's  law,  the  gas  will  have 
a  new  volume,  V,  given  by  the  equation  p^vQ  =  p-^f.  Then, 
keeping  the  pressure  constant  at  plt  alter  the  temperature  from 
T0  to  the  final  value  Tlf  the  final  volume,  vlt  will,  by  Gay-Lussac's 
law,  be  given  by  the  equation  V/T0  =  z^/Tj.  Substituting  in  the 
last  equation  the  value  of  V  obtained  from  the  former  equation 
(V  =  /VVA)  we  obtain 

A>»0      p-iV-i 

4-^  =-  ^-^  =  constant. 
LQ         Li 

This  may  be  written  in  the  form  pv  =  rT  where  r  is  a  constant ; 
in  other  words,  the  product  of  the  pressure  and  volume  of  a  gas 
is  proportional  to  the  absolute  temperature. 

At  a  definite  temperature  and  pressure,  the  volume  of  the 
gas,  and  consequently  the  value  of  r,  will  be  proportional  to 
the  quantity  of  gas  taken.  Further,  according  to  Avogadro's 
hypothesis,  the  molecular  weight  in  grams  of  all  gases  occupies 
the  same  volume  under  the  same  conditions.  It  follows  that  for 
these  quantities  the  constant  r  will  have  the  same  value  for  all 
gases,  quite  independent  of  the  conditions  under  which  the 
gases  are  measured.  This  special  value  of  the  constant  may 
conveniently  be  represented  by  R,  and  we  then  obtain  the 
equation 

PV  =  RT, 

where  V  is  the  volume  occupied  by  the  molecular  weight  of  a 
gas  in  grams,  at  the  absolute  temperature  T  and  under  the 
pressure  P — an  equation  which  is  of  fundamental  importance 
for  the  behaviour  of  gases  and  also  for  dilute  solutions.  The 
molecular  weight  of  a  gas  in  grams,  which,  according  to  the 
atomic  theory,  represents  the  weight  of  the  same  number  of 
molecules  in  each  case,  is  conveniently  termed  a  mol  (Ostwald). 


GASES  27 

The  numerical  value  of  R,  in  C.G.S.  units,  may  readily  be 
calculated  from  the  accurate  observations  of  the  densities  of 
gases  made  by  Regnault,  Rayleigh  and  others.  There  is,  how- 
ever, a  little  uncertainty  in  the  calculation  owing  to  the  fact  that 
the  volumes  occupied  by  a  mol  of  different  gases  under  equiva- 
lent conditions  are  not  quite  the  same,  although  very  nearly  so. 
Thus  2 -oi  6  grams  of  hydrogen,  32-00  grams  of  oxygen  and 
28-02  grams  of  nitrogen  occupy  22-43,  22-39  an^  22-40  litres 
respectively  at  o°  and  76  cms.  Taking  22-40  litres  as  a  mean 
value,  and  substituting  the  values  for  T  (273°)  and  P  (76  x 
13-59  =  1033-3  grams  per  sq.  cm.),  we  obtain 

PV     io-*v*  x  22,400 
R  =— =—     L^— =-84,76ogram-cms.  =  83^5,0,000.  ergs 

As  the  pressure  is  measured  in  gram/cm.2,  the  volume  is  of  the 
dimensions  cm.3,  and  T  is  merely  a  number,  the  above  value 
for  R  is  of  the  form  gram  x  cms.  or  gram-centimetres.  The 
calorie,  the  ordinary  heat  unit,  is  equal  to  42,640  gram-centi- 
metres =  41,830,000  ergs,  so  that  the  value  of  R  is  almost  ex- 
actly double  (accurately  1-99  times)  that  of  a  calorie.  We  may 
therefore  write  the  gas  equation  in  the  simplified  form  PV  = 
i'99T,  but  the  approximate  form  PV  =*  2T  is  sufficiently  accu- 
rate for  many  purposes.  In  this  form  the  gas  equation  is  repre- 
sented in  thermal  units. 

The  product  PV  in  the  gas  equation  is  of  the  nature  of  energy, 
as  is  clear  from  the  fact  that  when  a  volume,  v,  of  a  gas  is  gener- 
ated under  constant  external  pressure  (say  that  of  the  atmosphere) 
the  work  done  is  proportional  to  the  volume  and  to  the  pressure 
overcome,  and  therefore  to  their  product.  The  work  done  by 
or  upon  a  gas  when  it  changes  its  volume  under  a  constant  ex- 
ternal pressure  can  readily  be  obtained  in  thermal  units  by  using 
the  second  form  of  the  gas  equation  given  above.  Thus  if  a 
mol  of  a  gas  is  generated  at  o°  under  the  pressure  of  the  atmos- 
phere, the  amount  of  heat  absorbed  in  performing  the  external 
work  of  expansion,  PV,  is  2T  =  2  x  273  =  546  cal. 

Since  PV  is  constant,  the  pressure  under  which  a  definite 


28          OUTLINES  OF  PHYSICAL  CHEMISTRY 

mass  of  a  gas  is  generated  at  a  definite  temperature  has  no 
influence  on  the  external  work  of  expansion.  Thus,  to  take 
the  above  illustration,  if  a  mol  of  a  gas  is  generated  under  a 

pressure  of  —  atmosphere,  the  volume  will  be  22-4  x  10  =  224 

litres,  and  the  work  done  will  again  be  546  cal.  at  o°. 

Deviations  from  the  Gas  Laws— Careful  experiment 
shows  that  although  the  gas  laws,  which  are  summarised  in 
the  general  formula  PV  =  RT,  give  a  general  idea  of  the 
behaviour  of  gases,  yet  they  do  not  represent  accurately  the 
behaviour  of  any  single  gas,  the  deviations  depending  both  on 
the  conditions  of  observation  and  on  the  nature  of  the  gas. 
It  may  be  said,  in  general,  that  the  laws  are  the  more  nearly 
obeyed  the  higher  the  temperature  and  the  smaller  the  pressure, 
and,  as  regards  the  nature  of  the  gas,  the  further  it  is  removed 
from  the  temperature  of  liquefaction.  A  gas  which  would  follow 
the  gas  laws  accurately  is  called  a  perfect  or  ideal  gas,  and 
ordinary  gases  approach  more  or  less  nearly  to  this  ideal 
behaviour. 

The  accompanying  figure  (Fig.  i)  gives  a  graphic  representa- 
tion of  the  behaviour  of  the  three  typical  gases,  hydrogen, 
nitrogea  and  carbon  dioxide,  according  to  Amagat.  The  pro- 
duct PV,  in  arbitrary  units,  is  represented  on  the  vertical  axis 
and  the  pressure  P,  in  atmospheres,  along  the  horizontal  axis. 
If  PV  were  constant  (Boyle's  law),  the  curves  would  be  straight 
lines  parallel  to  the  horizontal  axis.  Actually,  PV  increases 
continuously  with  the  pressure  in  the  case  of  hydrogen,  and  for 
nitrogen  and  carbon  dioxide  it  first  decreases,  reaches  a  mini- 
mum, and  beyond  that  point  increases  with  increase  of  pres- 
sure. All  gases  except  hydrogen  show  a  minimum  in  the 
curve,  which  indicates  that  the  compressibility  is  at  first  greater 
than  corresponds  with  Boyle's  law,  reaches  a  point  (which  differs 
for  different  gases)  at  which  for  a  short  interval  Boyle's  law  is 
followed,  and  beyond  that  point  is  less  compressible  than  the 
law  indicates.  Hydrogen,  on  the  other  hand,  is  always  less 


GASES 


29 


compressible  than  the  law  requires  at  ordinary  temperatures, 
but  at  very  low  temperatures  it  would  also  probably  show  a 
minimum  in  the  curve.  That  the  deviations  from  the  simple 
law  become  less  the  higher  the  temperature,  is  very  well  illus- 
trated by  the  curves  for  carbon  dioxide  at  35*1°  and  100°. 


P  (.Metres  of  Mercury) 


20    40    60    80   100  120  140  160  1 80  200  220  240  260  280  300 
FIG.  i. 

The  general  behaviour  of  gases,  and  the  deviations  from  the 
simple  laws,  find  a  very  satisfactory  interpretation  on  the  basis 
of  the  kinetic  theory  of  gases,  which  we  are  now  to  consider. 

KINETIC  THEORY  OF  GASES 

General — The  fact  that  the  laws  followed  by  gases  are  so 
simple  in  character  makes  it  readily  intelligible  that  attempts 
to  account  for  their  properties  on  a  mechanical  basis  were 
made  very  early  in  the  history  of  science  (Bernoulli,  1738). 
Our  present  views  on  the  subject,  known  as  the  kinetic  theory 


30         OUTLINES  OF  PHYSICAL  CHEMISTRY 

of  gases,  are  due  more  particularly  to  the  labours  of  Clerk 
Maxwell,  Clausius  and  Boltzmann. 

According  to  the  theory,  gases  are  regarded  as  being  made 
up  of  small,  perfectly  elastic  particles  (the  chemical  molecules) 
which  are  in  continual  rapid  motion,  colliding  with  each  other 
and  with  the  walls  of  the  containing  vessel.  The  space  actually 
filled  by  the  gas  particles  is  supposed  to  be  small  compared  with 
that  which  they  inhabit  under  ordinary  conditions,  so  that  the 
particles  are  practically  free  from  each  other's  influence  except 
during  a  collision.  Owing  to  the  comparatively  large  free  space 
in  which  the  particles  move,  an  individual  particle  will  move  over 
a  certain  distance  before  colliding  with  another  particle ;  the 
average  value  of  this  distance  is  termed  the  "  mean  free  path  " 
of  the  molecule.  On  this  theory  the  pressure  exerted  by  the 
gas  on  the  walls  of  the  containing  vessel  (which  is  equal  to  the 
pressure  under  which  it  is  confined)  is  due  to  the  bombardment 
of  the  walls  of  the  vessel  by  the  moving  particles.  It  is  clear  that 
the  magnitude  of  the  pressure  must  depend  on  the  frequency 
of  the  collisions,  as  well  as  on  the  mass  and  velocity  of  the 
particles. 

Kinetic  Equation  for  Gases — The  pressure  exerted  by  a 
gas  can  be  calculated  quantitatively  in  terms  of  the  number 
and  velocity  of  the  molecules  as  follows  :  Imagine  a  definite 
mass  of  a  gas  contained  in  a  cube,  the  sides  of  which  are  of 
length  / ;  let  n  be  the  number  of  particles,  each  of  mass  m  and 
velocity  c.  The  particles  will  impinge  on  the  walls  in  all  direc- 
tions, but  the  velocity  of  each  may  be  resolved  into  three  com- 
ponents, x,  y  and  z,  parallel  to  the  edges  of  the  cube,  the 
components  being  related  to  the  original  velocity  c  by  the 
equation  x2  +  y2  +  z2  =  <?.  This  means  that  the  action  on 
the  wall  which  the  molecule  would  exert  if  it  reached  it  in  the 
original  path  with  the  velocity  c  is  the  same  as  the  sum  of  the  effects 
if  the  collisions  took  place  successively  in  directions  perpendicular 
to  the  three  walls  at  right  angles  to  each  other  with  the  velocities 
x,  y  and  z  respectively.  If  we  consider  at  first  one  of  the  com- 


GASES  31 

ponents,  the  particle  will  strike  the  wall  at  right  angles  with 
velocity  x,  and  will  fly  off  with  the  same  velocity  in  the  opposite 
direction :  as  the  wall  and  the  particle  are  considered  perfectly 
elastic,  there  will  be  no  loss  of  energy  in  this  process.  The 
momentum  before  the  impact  is  mx,  after  the  impact  —  mx,  so 
that  the  total  change  of  momentum  due  to  the  impact  is  2mx. 
As  the  distance  between  the  two  parallel  walls  is  /,  the  particle 

will  perform  -  impacts  on  the  walls  in  unit  time,  and  as  in  each  of 
these  the  change  of  momentum  is  2mx,  the  total  effect  of  a  single 
particle  in  one  direction  in  unit  time  will  be  2mx  -  =  2mx^jl. 

The  same  applies  to  the  other  components  of  the  velocity,  so 
that  the  total  action  of  a  molecule  on  all  six  sides  of  the  cube 

o 

is  - —  fa'2  +  y2  +  z2)  =  — -j —  For  the  total  number  of  mole- 
cules, n,  the  effect  is  therefore  2mnc2jl.  In  order  to  obtain 
the  pressure  on  unit  area,  the  above  value  must  be  divided  by 
the  total  interior  surface  of  the  cube,  6P ;  we  then  obtain  /  = 

2 

,  .3   >  which,  since  the  volume,  v,  of  the  cube  is  ^,  can  be  put 

in  the  more  convenient  form,  p  =  \mnfi '/v  or  pv  =  \mnc^. 

Although  the  above  expression  has  been  deduced  only  for 
a  cube,  it  can  readily  be  extended  to  a  vessel  of  any  shape,  as 
follows.  The  total  volume  of  the  latter  can  be  partitioned  up 
into  small  cubes,  and  as  the  pressures  on  the  two  sides  of  the 
interior  walls  of  these  cubes  neutralize  each  other,  they  do  not 
affect  the  pressure  on  the  outer  walls  of  the  exterior  cubes, 
which  in  the  limit  constitute  the  wall  of  the  containing  vessel. 

Deduction  of  Gas  Laws  from  the  Equation  pv  =  %mnc* 
— From  the  above  equation,  which  has  been  derived  on  certain 
more  or  less  plausible  assumptions  regarding  the  constitution  of 
gases,  some  of  the  laws  which  have  been  obtained  experimentally 
may  readily  be  deduced. 

Since  on  the  assumptions  made  in  deducing   the  general 


32          OUTLINES  OF  PHYSICAL  CHEMISTRY 

formula  the  right-hand  side  of  the  equation  is  made  up  of 
factors  which  are  constant  at  constant  temperature,  the  product 
of  pressure  and  volume  must  also  be  constant,  which  is  Boyle's 
law. 

Moreover,  the  above  equation  may  be  written  in  the  form 
pi)  =  I  .  ^mnfi.  As  shown  in  mechanics,  the  expression  \rnfi 
represents  the  kinetic  energy  of  a  particle  of  mass  m  and  velo- 
city c,  and  therefore  n  .  \mci  represents  the  kinetic  energy  of  n 
particles,  so  that  the  product  of  the  pressure  and  volume  of  a 
gas  is  equal  to  f  of  the  kinetic  energy  of  the  molecules.  From 
this  it  follows  that  for  equal  volumes  of  different  gases  under  the 
same  pressure,  the  total  kinetic  energy  of  their  molecules  is  the 
same. 

It  has  been  shown  (p.  25)  that  at  constant  volume  the  pres- 
sure of  a  gas  varies  proportionately  with  the  absolute  tempera- 
ture. In  the  previous  paragraph,  it  has  further  been  shown 
that  at  constant  volume  the  pressure  of  a  gas  is  proportional 
to  the  mean  kinetic  energy  of  progressive  motion  of  its  particles. 
Hence  the  mean  kinetic  energy  of  the  molecules  of  a  gas  is  pro- 
portional to  its  absolute  temperature}- 

Avogadro's  hypothesis  may  now  be  deduced  from  the  kinetic 
theory.  For  equal  volumes  of  two  gases  at  the  same  pressure 
we  have,  from  the  above  equation, 

fr+lftmtf^-inpjff     .        .  (i) 

where  n^  and  n2,  ml  and  m2  and  ^  and  <r2  represent  the  number, 
mass  and  velocity  of  the  molecules  of  the  respective  gases- 
Further,  if  the  gases  are  at  the  same  temperature,  the  mean 
kinetic  energy  of  a  single  molecule  is  the  same  for  each  gas,2 
hence 


Dividing  equation  (i)  by  equation  (2)  we  obtain  n^  =  n%  or, 
otherwise  expressed,  equal  volumes  of  two  gases,  under  the  same 

1  In  this  case,  instead  of  deducing  the  experimental  law  from  the  kinetic 
theory,  we  have  made  use  of  the  experimental  result  to  obtain  a  definition 
of  temperature  on  the  kinetic  theory.     The  temperature  of  a  gas  is  deter- 
mined by  the  mean  kinetic  energy  of  progressive  movement  of  its  molecules. 

2  This  was  proved  by  Clerk  Maxwell  ;  it  does  not  follow  directly  from 
the  above  statement. 


GASES  33 

conditions  of  temperature  and  pressure,  contain  the  same  num- 
ber of  molecules,  which  is  Avogadro's  hypothesis. 

Finally,  the  mean  velocity,  c,  of  the  molecules  1  may  be  cal- 
culated by  substituting  the  appropriate  values  for  the  other 
magnitudes  in  the  general  equation  pv  =  \rnnc1.  Thus  for  i 
mol — 2 -oi  6  grams — of  hydrogen  under  standard  conditions, 
P  =  I033'3  gram/cm.2  or  1033-3  x  9Sl  dynes,  mn  =  2-016 
grams,  v  —  22,400  c.c.,  we  have 

=     /3  x  1033-3  x   980-6  x  22,400  =  i83>9Qo 

cm.  per  sec.  Therefore  the  molecule  of  hydrogen  moves  at  o°  at 
the  enormous  speed  of  1*839  kilometres  or  rather  more  than  i 
mile  per  second.  The  magnitude  of  this  velocity  may  seem 
surprising,  in  view  of  the  fact  that  the  diffusion  of  gases,  which 
on  the  kinetic  theory  is  conditioned  by  the  speed  of  the  mole- 
cules, is  comparatively  slow,  but  it  must  be  borne  in  mind  that 
this  speed  is  only  attained  in  the  "  free  path,"  and  owing  to 
collisions  and  consequent  change  of  path,  the  actual  progress  of 
a  particle  is  very  much  less.  The  average  speed  of  the  mole- 
cules of  any  other  gas  may  be  calculated  by  substitution  in  a 
similar  way.  It  is  clear  from  the  form  of  the  equation  (mnjv  =  d) 
that  at  constant  temperature,  the  rates  are  inversely  proportional 
to  the  square  root  of  the  densities  of  the  different  gases — a  result 
which  is  connected  with  the  laws  of  gaseous  diffusion  (Graham's 
law)  and  of  gaseous  effusion. 

Van  der  Waals'  Equation — The  kinetic  theory  of  gases 
not  only  admits  of  a  simple  deduction  of  the  gas  laws,  but  also 
gives  a  plausible  explanation  of  the  deviation  of  gases  from  the 
simple  laws,  discussed  in  the  previous  sections.  In  deducing 
Boyle's  law  in  the  previous  section  two  simplifying  assumptions 
have  been  made  which  are  not  strictly  justifiable.  In  the  first 
place,  it  has  been  assumed  that  in  its  motion  backwards  and  for- 

For  a  full  discussion  of  the  kinetic  theory  of  gases,  more  particularly 
with  reference  to  the  different  velocities  of  the  individual  particles,  see 
O.  E.  Meyer,  Kinetic  Theory  of  Gases  (Longmans,  1899). 
3 


34          GUI  LINES  OF  PHYSICAL  CHEMISTRY 

wards  between  the  opposite  walls  of  the  cube,  the  molecule  has  the 
whole  length  available  for  its  motion,  but  a  little  consideration 
shows  that,  if  the  size  of  the  molecule  is  not  negligible  in  com- 
parison with  this  distance,  the  number  of  impacts  on  the  walls, 
and  therefore  the  pressure  of  the  gas,  is  greater  than  it  would  be 
on  the  original  assumption.  To  take  an  extreme  case,  let  us 
assume  that  the  distance  between  the  walls  is  20  times  that  of 
the  diameter  of  the  molecule,  the  space  available  for  movement 
is  only  19  molecular  diameters,  and  therefore  the  pressure  will 
be  greater,  in  the  ratio  of  20  :  19,  than  if  the  size  of  the  molecule 
could  be  neglected.  This  error  will  clearly  be  negligible  at  low 
pressures  (when  the  total  volume  is  large)  but  will  become  im- 
portant when  the  gas  is  strongly  compressed.  If  b  is  the 
volume  occupied  by  the  molecules,  it  seems  plausible  to  correct 
the  general  gas  equation,  PV  =  RT,  by  substituting  for  V,  the 
total  volume  occupied  by  the  gas,  V  -  b,  the  "  free  "  volume  avail- 
able for  the  movement  of  the  molecules,  so  that  the  general  gas 
equation  becomes  P(V  -  b)  =  RT.  In  reality,  for  reasons 
which  cannot  be  entered  into  here,  b  must  be  taken,  not  as 
the  volume  filled  by  the  material  of  the  molecules,  but  as  a 
multiple  of  it,  the  actual  magnitude  of  which  is  uncertain. 

Another  tacit  assumption  we  have  made  in  deducing  Boyle's 
law  is  that  the  gas  particles  exert  no  mutual  attraction,  an 
assumption  which  is  not  justified  when  the  gas  is  strongly  com- 
pressed. A  little  consideration  shows  that  when  increased 
pressure  is  applied  to  a  gas,  the  resulting  volume  will  be  less 
than  the  calculated  value  owing  to  molecular  attraction ;  in 
other  words,  the  gas  behaves  as  if  the  pressure  applied  is  greater 
than  it  actually  is.  It  was  shown  by  van  der  Waals  that  this 
correction  is  inversely  proportional  to  the  square  of  the  volume, 
and  as,  from  the  above  considerations,  it  affects  the  gas  as  an 
increase  of  pressure,  we  must  substitute  for  P,  in  the  gas  equation, 

the  expression  P  +  y^  where  a  is  a  constant.      The  corrected 
gas  equation  then  becomes 


GASES  35 


an  expression,  first  proposed  by  van  der  Waals  (1879),  which 
not  only  represents  with  fair  accuracy  the  behaviour  of  strongly 
compressed  gases,  but  throws  considerable  light  on  the  con- 
stitution of  liquids.  The  detailed  consideration  of  van  der 
Waals'  equation  is  postponed  to  the  next  chapter  (p.  53)  to 
which  it  more  properly  belongs  ;  at  present  it  will  be  sufficient 
to  show  that  it  affords  a  satisfactory  qualitative  explanation  of 
the  deviations  from  the  gas  laws,  discussed  on  page  28. 

When  V  is  very  large,  b  will  be  negligible  in  comparison  and 
#/V2  will  be  very  small,  so  that  van  der  Waals'  equation  then 
approximates  to  the  simple  gas  equation  PV  =  RT.  It  may 
therefore  be  expected  that  any  influence  which  tends  to  increase 
the  volume,  such  as  raising  the  temperature  at  constant  pressure, 
or  diminishing  the  pressure  at  constant  temperature,  will  affect 
the  gas  in  such  a  way  that  it  follows  the  simple  gas  laws  more 
closely,  and  this  expectation  is  quite  borne  out  by  the  results  of 
experiment  (p.  29).  Further,  we  can  employ  the  equation  to 
explain  the  fact  already  referred  to,  that  PV  for  all  gases  except 
hydrogen  at  first  diminishes  with  increasing  pressure,  reaches  a 
minimum  value,  and  beyond  that  point  increases  steadily  as  far 
as  the  observations  extend.  From  the  form  of  van  der  Waals' 
equation  it  is  clear  that  the  volume  correction  acts  in  the 
opposite  direction  to  that  for  the  attraction,  the  value  of  PV 
being  increased  by  the  former  and  diminished  by  the  latter. 
At  low  pressures  the  effect  of  the  attraction  preponderates, 
whilst  at  high  pressures  the  latter  is  negligible  in  comparison 
with  the  volume  correction.  At  some  intermediate  pressure 
(about  50  metres  for  nitrogen  at  30°  ;  see  Fig.  i)  the  two  cor- 
rections just  balance,  and  in  this  short  region  the  gas  exactly 
follows  Boyle's  law. 

To  explain  the  behaviour  of  hydrogen,  it  is  assumed  that  the 
attraction  correction  at  ordinary  temperatures  is  from  the  first 
counterbalanced  by  the  volume  correction. 


36          OUTLINES  OF  PHYSICAL  CHEMISTRY 

AVOGADRO'S  HYPOTHESIS  AND  THE  MOLECULAR  WEIGHT 
OF  GASES 

General  —  As  we  have  already  learnt,  the  application  of 
Avogadro's  hypothesis  permits  of  the  determination  of  the 
molecular  weight  of  any  substance  which  can  be  obtained  in 
the  gaseous  form;  it  is  only  necessary  to  find  the  weight  in 
grams  of  the  substance  in  question  which  occupies  in  the 
gaseous  form  a  volume  of  22-40  litres  at  o°  and  76  cm.  pressure. 
In  determining  molecular  weights  by  this  method,  it  is  neither 
necessary  nor  practicable  to  work  at  the  temperature  or  under 
the  pressure  referred  to  ;  in  practice  the  volume  occupied  by 
a  known  weight  of  the  gas  or  vapour  under  suitable  and  known 
conditions  of  temperature  and  pressure  is  determined,  then  with 
the  help  of  the  gas  laws  the  weight  in  grams  which  will  occupy 
22*40  litres  under  standard  conditions  is  determined.  Suppose 
it  is  found  that  g  grams  of  a  gas  or  vapour  occupy  v  c.c.  at 
T°  Abs.  and  /  millimetres  pressure,  what  weight  in  grams  will 
occupy  22,400  c.c.  at  273°  Abs.  and  760  mm.  pressure? 

It  has  already  been  shown  (p.  26)  that  the  expression  /#/T 
is  proportional  to   the   mass  of  the  gas,   independent  of  the 
conditions  under  which  it  is  measured.     It  follows  that 
^pv_       M        760  x  22,400 

where  M  is  the  molecular  weight  of  the  gas  in  grams.     Hence 
M_£"x  76o  x  22,400  x  (273  +  /°C.)  ^ 

273  x/x  v 

A  shorter  method  is  to  use  the  alternative  expression  for  the 
gas  equation  l  pv  =  n  RT,  where  n  represents  the  number  of 
gram-  molecules  of  gas  in  the  volume  v.  Since  n  =£/M  we  have 


pv 
Density  and  Molecular  Weight  of  Gases  and  Vapours 

—  The  determination   of  the   volume   occupied   by  a   known 

1  Care  must  be  taken  to  express  R  in  the  proper  units,  corresponding 
with  those  in  which  the  pressure  and  volume  are  given.  (Cf.  p.  in.) 


GASES  37 

weight  of  a  gas  or  vapour  under  definite  conditions  is  equivalent 
to  determining  its  density,  which  is  the  mass  per  unit  volume. 
The  actual  determinations  may  be  made  in  various  ways.  It 
will  be  sufficient  for  our  present  purpose  to  describe  Regnault's 
method,  which  is  particularly  suitable  for  the  permanent  gases, 
and  the  method  first  suggested  by  Victor  Meyer,  which  is 
now  used  almost  exclusively  for  determining  the  density,  and 
therefore  the  molecular  weight,  of  vapours. 

(1)  Regnaults  Method — Two  glass  bulbs  of  approximately 
equal  capacity  and   provided  with  well-ground  stop-cocks  are 
used.     One  is  exhausted  as  completely  as  possible  by  means 
of  a  pump,  weighed,  filled  at  a  known  temperature  and  pressure 
with  the  gas  the  density  of  which  has  to  be  determined,  and 
again  weighed,  the  other  bulb  being  used  as  counterpoise.    The 
volume  of  the  bulb  may  be  obtained  by  weighing  it  empty  and 
then  filled  with  distilled  water  at  a  known  temperature.     One 
of  the  advantages  of  using  a  second  bulb  is  that  any  risk  of 
error  arising  from  a  change  in    the  temperature,  pressure  or 
humidity  of  the  air  in  the  balance-case  during  the  weighing 
is  avoided.     From  the  results,  the  density  referred  to  hydrogen 
as  unity  can  readily  be  calculated,  and  hence  the  molecular  weight, 
which  is  double  the  density  (p.  10).    The  molecular,  weight  can 
also  be  obtained  by  substituting  in  the  formula  given  above. 
This  method,  with  slight  modifications,  has  been  employed  in 
recent  years  by  Lord  Rayleigh,  Morley,  Ramsay  and  others  for 
determining  the  densities  of  the  permanent  gases,  and  is  cap- 
able of  giving  results  of  the  highest  accuracy. 

(2)  Victor  Meyer  s  Method—  This  method  differs  from  all  the 
others  inasmuch  as  it  is  not  the  volume  of  the  vapour  itself 
which  is  measured,  but  that  of  an  equal  volume  of  air  which 
has  been  displaced  by  the  vapour. 

The  apparatus  consists  of  a  cylindrical  vessel,  A,  of  about 
200  c.c.  capacity,  ending  in  a  long  neck  provided  with  two 
side  tubes,  as  shown  in  Fig.  2.  One  of  these  side  tubes,  /, 
from  which  the  displaced  air  issues  during  an  experiment,  is 


OUTLINES  OF  PHYSICAL  CHEMISTRY 


bent  in  such  a  way  that  its  free  end  can  conveniently  be  brought 
under  the  surface  of  water  in  a  suitable  vessel.  Into  the  other 
tube,  /2,  fits  a  rubber  tube  enclosing  a  glass  rod  which  can  be 
moved  outwards  and  inwards,  and,  at  the  commencement  of  the 
experiment,  serves  to  retain  in  place  the  small  glass  bulb  shown 
in  the  figure,  containing  a  weighed  quantity  of  the  liquid,  the 
vapour  density  of  which  is  to  be  determined.  The  top  of  the 
main  tube  is  closed  by  a  cork  which  is  kept  in  place  throughout 
an  experiment,  and  a  little  asbestos  or 
mercury  is  placed  in  the  bottom  to  guard 
against  fracture  of  the  glass  when  the  bulb 
drops.  The  apparatus  is  heated  at  a  con- 
stant temperature  throughout  the  greater 
part  of  its  length  by  means  of  the  vapour 
of  a  liquid  boiling  in  the  outer  bulb-tube, 
B  ;  the  temperature  should  be  at  least  20° 
above  the  boiling  point  of  the  liquid  to 
be  vaporized. 

At  the  commencement  of  an  experi- 
ment, the  bulb  and  rod  are  placed  in 
position  and  the  cork  inserted,  the  jacket- 
ing liquid  is  then  boiled  till  air  ceases  to 
issue  from  the  end  of  the  tube,  /,  and 
bubble  through  the  water,  showing  that 
the  temperature  inside  the  bulb,  A,  is 
constant.  A  graduated  measuring  tube, 
C,  full  of  water,  is  then  inverted  over  the  end  of  the  delivery 
tube,  and  the  small  bulb  allowed  to  drop  by  drawing  back 
the  glass  rod.  When  air  ceases  to  issue  from  the  end  of  the 
delivery  tube,  the  graduated  tube  is  closed  by  the  thumb, 
removed  to  a  deep  vessel  containing  water,  allowed  to  stand 
till  the  temperature  is  constant,  and  the  volume  of  air  read  off 
when  the  water  outside  and  inside  are  at  the  same  level. 

The  temperature  inside  the  tube,  A,  is  the  same  before  and 
after  the  experiment,  the  only  difference  in  the  conditions  is 


GASES  39 

that  a  certain  volume  of  air  is  displaced  by  an  equal  volume 
of  vapour.  The  observed  volume  of  air  is  therefore  that  which 
the  vapour  would  occupy  after  reduction  to  the  temperature 
and  pressure  at  which  the  air  is  measured  (provided  that  the 
vapour  and  air  are  equally  affected  by  changes  of  temperature 
and  pressure,  which  is  approximately  the  case  under  suitable 
conditions).  The  temperature  is  that  of  the  water,  and  the 
pressure  that  of  the  atmosphere  less  the  vapour  pressure  of 
water  at  the  temperature  of  observation.  It  is  clear  that  it  is 
not  necessary  to  know  the  temperature  at  which  the  substance 
is  vaporized,  and  this  is  one  of  the  advantages  of  the  method. 

The  mode  of  calculating  molecular  weights  from  the  observed 
data  may  be  illustrated  by  the  following  example:  0-220  grams 
of  chloroform  when  vaporized  displaced  45*0  c.c.  of  air, 
measured  at  20°  and  755  mm.  pressure.  As  the  vapour 
pressure  of  water  at  20°  is  17-4  mm.,  the  actual  pressure 
exerted  by  the  gas  is  755-  17 '4  =  737 '6  mm.  Therefore,  as 
0-220  grams  of  vapour,  at  20°  and  737*6  mm.  pressure,  occupy 
45-0  c.c.,  we  have  to  find  what  weight  in  grams  will  occupy 
22,400  c.c.,  at  273°  abs.  and  760  mm.  pressure,  and  this  will 
be  the  required  molecular  weight.  Substituting  in  the  general 
formula  (p.  36)  we  have 

_  0*2 20  x  760  x  22,400  x  (273  +  20) 

273x737-6x45  [I7' 

This  result  is  in  fair  agreement  with  the  molecular  weight 
of  chloroform  (119*5)  calculated  from  its  formula. 

The  results  obtained  by  this  method  are  only  accurate  if  the 
vapour  follows  the  gas  laws  as  closely  as  air  (since  only  under 
these  circumstances  will  the  vapour  replace  an  exactly  equivalent 
quantity  of  air),  and  as  the  vapour  is  often  not  very  remote 
from  its  temperature  of  condensation,  this  condition  is  not  in 
general  fulfilled.  In  the  great  majority  of  cases,  however,  the 
results  are  sufficiently  near  for  the  purpose,  as  the  composition 
of  the  substance  can  be  determined  with  great  accuracy  by 
chemical  analysis,  and  the  vapour  density  method  is  only  used 


40         OUTLINES  OF  PHYSICAL  CHEMISTRY 

to  distinguish  between  simply  related  numbers.  In  the  example 
given  above,  for  instance,  analysis  shows  that  the  molecular 
weight  of  chloroform  must  be  HQ'5  or  a  simple  multiple  of 
that  number,  and  the  density  determination  proves  that  the 
former  alternative  is  correct. 

Results  of  Yapour  Density  Determinations.  Ab- 
normal Molecular  Weights— The  most  important  result  of 
the  numerous  molecular  weight  determinations  which  have  been 
made  by  this  method  is  that  in  general  the  values  obtained  are 
in  complete  agreement  with  those  based  on  chemical  considera- 
tions. There  are  certain  exceptions  to  this  rule,  but  for  all 
these  plausible  explanations  have  been  suggested.  In  the  case 
of  elements,  the  values  found  are  simple  multiples  of  the  atomic 
weights  (very  often  twice  the  atomic  weight),  whilst  in  the  case 
of  compounds  they  are  simple  multiples  of  the  sum  of  the 
atomic  weights. 

All  the  metals  which  have  been  obtained  in  gaseous  form, 
including  mercury,  zinc,  cadmium,  potassium,  sodium,  antimony 
and  bismuth,1  are  monatomic,  as  are  the  rare  elements  argon, 
helium,  krypton,  etc.,  discovered  in  the  atmosphere  by  Ramsay 
and  his  co-workers.  "-Many  of  the  non-metals,  such  as  oxygen, 
nitrogen  and  chlorine,  are  diatomic  under  ordinary  conditions. 
Whilst  arsenic  and  phosphorus  are  tetratomic,  sulphur  at  low 
temperatures  gives  results  corresponding  with  the  formula  S8. 
Several  elements,  such  as  carbon  and  silicon,  and  many  metals 
have  not  yet  been  obtained  in  the  gaseous  form. 

The  determination  of  molecular  weights  at  high  temperatures 
has  been  greatly  developed  in  recent  years,  more  particularly 
by  Victor  Meyer  and  his  co-workers,  and  by  Nernst.  The  air- 
displacement  method  has  proved  most  suitable  for  this  purpose, 
but  the  chief  difficulty  has  been  to  obtain  vessels  which  stand 
high  temperatures,  and  are  not  porous  for  the  contained 
vapours.  Victor  Meyer  at  first  replaced  glass  by  porcelain, 

1  Compare  H.  von  Wartenberg,  Zeitsch.  anorg.  Ghent.,  1907,  56,  320; 
Abstracts  Chem.  Society,  1908,  ii.,  86. 


GASES  41 

and  the  latter  by  an  alloy  of  platinum  and  iridium,  and  at  the 
time  of  his  death  was  experimenting  with  vessels  of  magnesium 
oxide.  Satisfactory  results  were  obtained  up  to  1700-1800°. 

One  of  the  most  striking  results  obtained  by  Victor  Meyer  is 
that  the  molecular  weight  of  iodine,  which  at  600°  corresponds 
with  the  formula  I2,  becomes  smaller  as  the  temperature  is 
further  raised,  until  at  1500°  it  reaches  half  the  initial  value, 
indicating  that  at  the  latter  temperature  it  is  completely  split 
up  into  iodine  atoms.  Bromine  is  also  partially  decomposed 
at  1500°,  and  chlorine  commences  to  split  up  about  the  same 
temperature.  It  had  previously  been  shown  by  Deville  and 
Troost  that  the  molecular  weight  of  sulphur  also  diminishes 
with  increasing  temperature,  and  above  800°  gives  results  which 
indicate  that  only  diatomic  molecules  are  present. 

Nernst l  has  quite  recently  succeeded  in  extending  this  method 
up  to  2000°  by  using  a  vessel  of  iridium  coated  outside  and 
inside  with  a  paste  of  magnesia  and  magnesium  chloride, 
and  heated  in  an  electric  furnace.  At  this  temperature,  the 
molecular  weight  of  mercury  is  201,  indicating  that  the  atoms  of 
this  element  have  undergone  no  further  simplification,  whilst 
sulphur,  between  1800°  and  2000°,  has  a  density  of  about  24, 
indicating  that  the  diatomic  molecules  are  split  up,  to  the  ex- 
tent of  about  33  per  cent.,  into  single  atoms. 

Association  and  Dissociation  in  Gases — We  have  al- 
ready seen  that  such  substances  as  sulphur  and  arsenic  have 
abnormally  high  molecular  weights  at  low  temperatures ;  such 
substances  are  said  to  be  associated.  This  peculiarity  is  not 
confined  to  elements,  as  the  molecular  weight  of  acetic  acid, 
which,  as  determined  by  chemical  methods,  is  60,  exceeds  100 
when  determined  by  the  vapour  density  method  at  comparatively 
low  temperatures.  The  conclusion  that  acetic  acid  in  the  form 
of  vapour  at  comparatively  low  temperatures  consists  largely  of 
double  molecules  (CH3COOH)2,  is  in  satisfactory  agreement 
with  other  considerations. 

1  Compare  Wartenberg,  he.  cit. 


42         OUTLINES  OF  PHYSICAL  CHEMISTRY 

An  apparent  deviation  from  Avogadro's  hypothesis  of  a 
different  nature  is  met  with,  for  example,  in  the  case  of  gaseous 
ammonium  chloride.  On  chemical  grounds,  the  molecular 
formula,  NH4C1,  is  given  to  this  substance,  corresponding  with 
a  molecular  weight  of  53*5,  whereas  the  observed  value,  obtained 
from  its  vapour  density,  is  only  half  as  great.  This  behaviour 
could  be  accounted  for  on  the  assumption  that,  at  the  tem- 
perature of  the  experiment,  the  molecule  is  to  a  great  extent 
split  up,  or  dissociated,  into  NH3  and  HC1  molecules,  and 
the  experimental  justification  for  this  assumption  has  been 
obtained  by  Pebal  (1862),  who  effected  a  partial  separation 
of  the  decomposition  products  by  taking  advantage  of  their 
different  rates  of  diffusion. 

It  may  be  added  that  in  the  complete  absence  of  moisture, 
ammonium  chloride  can  be  vaporized  without  dissociation,  and 
then  has  the  normal  molecular  weight  deduced  by  means  of 
Avogadro's  hypothesis.1 

Accurate  Determination  of  Molecular  and  Atomic 
Weights  from  Gas  Densities— We  have  seen  that  Avogadro's 
hypothesis  does  not  hold  strictly  for  actual  gases,  and  that  the 
reason  for  this  is  probably  to  be  found  in  the  mutual  attractions 
and  finite  volumes  of  the  gas  particles.  We  may,  therefore, 
assume  that  it  would  be  strictly  true  for  an  ideal  gas,  and,  on 
the  basis  of  van  der  Waals'  equation,  apply  a  correction  to 
actual  gases  to  find  their  true  molecular  weights,  that  is,  the 
relative  masses  which  would  occupy  equal  volumes  at  great 
rarefaction,  when  the  gas  laws  would  be  strictly  followed  (p.  28). 
The  method  followed  is  therefore  to  determine  the  volume  of 
a  definite  mass  of  a  gas  under  two  or  more  pressures  (the 
compressibility  of  the  gas),  and  find  by  extrapolation  the  relative 
densities  of  different  gases  as  the  pressure  approaches  zero. 
This  method  has  been  used  more  particularly  by  Daniel 
Berthelotand  by  Lord  Rayleigh.  From  the  results,  the  follow- 

*H.  Brereton  Baker,  Trans.  Chem.  Society,  1894,  65,  611 ;  1898,73, 
422.  Compare  Johnston,  Zeitsch.  physikal  Chem.,  1908,  61,  457. 


GASES  43 

ing  molecular  weights  (vapour  density  x  2)  were  calculated  by 
Berthelot  (oxygen  =  32  being  taken  as  the  standard)  : — 

H2  N2          CO          O2          CO2        N2O       HC1 

2*0145     28*013    28*007    32*000    44*000    44*000    36*486 

From  these  observations,  the  following  atomic  weights  have 
been  obtained,  the  values  derived  by  chemical  methods  being 
placed  below  for  comparison  : — 

O  H  C  N  Cl 

Gas  density   16*000    1*0075    12*000    14*005    35*479 
Chemical       16*000    1*008      12*00      14*01      35'45 

The  agreement,  except  in  the  case  of  chlorine,  is  excellent, 
As  a  matter  of  fact,  the  chemical  value  for  chlorine  is  probably 
too  low  ;  the  recent  investigations  of  Richards  and  Wells l  appear 
to  show  that  the  true  value  is  35*473,  almost  identical  with  that 
obtained  by  the  density  method. 

The  above  striking  results  lend  strong  support  to  the  assump- 
tion that  in  the  limit  Avogadro's  hypothesis  is  strictly  valid  for 
all  gases. 

SPECIFIC  HEAT  OF  GASES 

General — The  specific  heat  of  any  substance  may  be  defined 
as  the  ratio  of  the  amounts  of  heat  required  to  raise  i  gram  of 
the  substance  in  question  and  i  gram  of  water  through  a  given 
range  of  temperature.  The  amount  of  heat  required  to  raise  i 
gram  of  water  i°  in  temperature  is  termed  a  calorie,  and  hence 
the  specific  heat  may  also  be  defined  as  the  quantity  of  heat  in 
calories  required  to  raise  i  gram  of  the  substance  i°  in  tem- 
perature. This  statement  has  only  a  definite  meaning,  however, 
when  the  conditions  under  which  the  heating  is  carried  out 
are  stated,  and  this  is  particularly  true  of  gases.  If  a  gas  is 
suddenly  compressed  it  becomes  warmer,  although  no  heat  has 
been  supplied  to  it,  and,  conversely,  if  a  gas  is  allowed  to  expand 
against  pressure  it  becomes  cooled,  although  no  heat  has  been 
abstracted  from  it.  According  to  the  above  definition, 
1  y.  A  mer.  Chem.  Soc.,  1905,  27,  459. 


44         OUTLINES  OF  PHYSICAL  CHEMISTRY 

amount  of  heat  supplied 
Specific  heat  =  — — 

rise  in  temperature 

so  that  if  a  gas  is  warmed  by  compression  its  specific  heat  is  zero. 
Moreover,  if,  while  a  gas  is  expanding  against  pressure,  sufficient 
heat  is  supplied  to  keep  its  temperature  constant,  the  heat 
supplied  has  a  certain  finite  value  whilst  the  change  of  tempera- 
ture is  zero,  so  that  the  specific  heat,  according  to  definition,  is 
infinite.  It  is  clear  that  the  specific  heat  of  a  gas  may  have  any 
value  whatever,  unless  the  conditions  under  which  it  is  measured 
are  stated. 

Specific  Heat  at  Constant  Pressure,  C,,.  and  Constant 
Volume,  Cv — There  are  two  important  cases  in  which  the  term 
"  specific  heat  of  a  gas  "  is  clearly  defined  :  (a)  the  specific  heat 
at  constant  volume,  Cw  (b)  the  specific  heat  at  constant  pressurs, 
Cp.  In  the  former  case,  the  volume  is  kept  constant  whilst 
the  gas  is  being  heated,  and  no  external  work  is  done.  In  the 
latter  case,  the  volume  is  allowed  to  increase  whilst  heat  is  being 
supplied,  work  is  therefore  done  against  the  pressure  of  the 
atmosphere,  which  tends  to  cool  the  gas.  Sufficient  heat  must 
therefore  be  supplied  not  only  to  raise  the  temperature,  but  to 
make  up  for  the  cooling  due  to  the  external  work  performed. 
It  is  clear  that  the  specific  heat  at  constant  pressure  is  greater 
than  that  at  constant  volume,  and  the  difference  is  the  heat  equi- 
valent of  the  amount  of  work  done  against  the  external  pressure. 

The  difference  between  the  two  specific  heats  may  readily  be 
obtained  in  thermal  units  by  using  the  general  gas  equation. 
For  this  purpose,  it  is  convenient  to  deal  with  a  mol  of  a  gas. 
It  has  already  been  shown  (p.  27)  that  when  a  gas  expands  at 
constant  pressure,  the  work  done  is  measured  by  the  product  of 
the  pressure  and  the  change  of  volume.  If  at  first  the  absolute 
temperature  is  Tx,  we  have  the  equation  PVj  =  RTX  where  Vl  is 
the  molecular  volume.  If  the  temperature  is  raised  to  T2,  and 
the  new  molecular  volume  is  V2,  the  work  done  during  the 
expansion  is 

P(V2-V1) 


GASES 


45 


In  the  present  case,  T2  -  Tx  is  i°,  therefore  P(V2  -  Vj)  =  R. 
Further,  the  difference  in  the  molecular  heats  of  a  gas  at 
constant  pressure  and  constant  volume  is  the  external  work 
done  when  a  mol  of  gas  is  raised  i°  in  temperature,  and  there- 
fore M  (CP  —  Cv)  (where  M  is  the  molecular  weight  of  the  gas) 
is  also  =  P  (V2  -  VJ.  Hence  M  (C  -  C.)  =  R.  In  thermal 
units,  R  is  approximately  2  calories,  so  that  the  difference  of 
the  specific  heats  of  a  mol  of  any  gas — in  other  words,  the 
difference  of  the  molecular  heats  of  any  gas  at  constant  pressure 
and  at  constant  volume — is  2  calories. 

The  specific  heat  of  a  gas  at  constant  pressure  can  readily  be 
determined  by  passing  a  known  quantity  of  it,  heated  to  a 
definite  temperature,  through  a  metallic  worm  in  a  calorimeter, 
at  such  a  rate  that  there  is  a  constant  difference  of  temperature 
between  the  entering  and  issuing  gas.  It  is  more  difficult  to 
determine  directly  the  specific  heat  at  constant  volume,  and  this 
has  only  been  accomplished  satisfactorily  in  comparatively  recent 
times.1 

The  molecular  heats  MC8  and  MQ,  (molecular  weight  x 
specific  heat)  of  a  few  of  the  commoner  gases  are  given  in  the 
accompanying  table,  the  values  of  C9  being  obtained  from  those 
of  Cp  by  subtracting  2  calories  : — 


Specific 

Gas. 

Heat, 
C, 

MC, 

IIC, 

CWC. 

•66 

Helium 







•66 

Mercury 

— 

— 

2-965 

•66 

Hydrogen 

3'4°9 

6-880 

4-880 

•412 

Oxygen 

0-2175 

6-960 

4-960 

•40 

Chlorine 

0-1241 

8-820 

6-820 

•29 

Hydrochloric  acid 

0-1876 

6-84 

4-84 

•409 

Nitrous  oxide 

0-2262 

9-99 

7-99 

•247 

Ether    . 

0-4797 

35-51 

33-5I 

i  -060 

^oly,  Proc.  Rov.  Soc.,  1889,47,218.     Compare  Preston,  Theory  of 
Heat,  p.  239, 


46          OUTLINES  OF  PHYSICAL  CHEMISTRY 

For  diatomic  molecules,  the  average  value  of  the  molecular 
heat  at  constant  volume  is  about  4-8  calories  in  the  neighbour- 
hood of  1 00° ;  but  chlorine  and  bromine  are  exceptions.  P'or 
triatomic  molecules  the  average  value  of  MC,  is  6 '5  cal.  and 
the  value  increases  with  the  complexity  of  the  compound,  as  is 
illustrated  in  the  table. 

Specific  Heat  of  Gases  and  the  Kinetic  Theory- 
Much  light  is  thrown  on  the  question  of  the  specific  heat  of 
gases  by  the  kinetic  theory.  According  to  this  theory  the 
energy-content  of  a  gas  is  made  up  of  three  parts:  (i)  the 
energy  of  rectilineal  (progressive  motion  of  the  molecules),  the 
so-called  kinetic  energy  (p.  32) ;  (2)  the  energy  of  intramolecular 
motion ;  (3)  the  potential  energy  due  to  the  mutual  action  of 
the  atoms;1  and  when  heat  is  supplied  to  a  gas  at  constant 
volume  all  three  factors  of  the  energy  may  be  affected.  For 
monatomic  gases,  however,  such  as  mercury  vapour,  the  factors 
(2)  and  (3)  are  presumably  absent,  and  the  heat  supplied  must 
simply  be  employed  in  increasing  the  kinetic  energy  of  the 
molecules.  We  have  already  learnt  (p.  32)  that  the  kinetic  energy 
of  i  mol  of  any  gas  =  f  PV  =  3T  if.  expressed  in  thermal  units. 
When  a  gas  is  raised  at  constant  volume  from  the  absolute 
temperature  T1  to  T2  we  have  for  the  kinetic  energies  at  the 
two  temperatures  the  equations  f  PjV  =  3^  and  f  P2V  =  3T2, 
where  Pl  and  P2  are  the  pressures  at  Tx  and  T2  respectively. 
Subtracting  the  first  equation  from  the  second,  we  obtain 
f  (P2~pi)v  =  3(T2~T1)  and  for  a  rise  of  temperature  of  i° 
f  (pa  ~  pi)v  =  3  (calories).  Therefore  the  molecular  kinetic 
energy  of  a  monatomic  gas  is  increased  by  3  calories  for  a  rise  of 
i°  in  temperature,  or,  in  other  words,  the  molecular  heat  MC, 
of  a  monatomic  gas  at  constant  volume  is  3  calories.  As  the 
specific  heat  at  constant  pressure  is  3  +  2  =  5  calories,  the  ratio, 
MCP/MQ,,  for  a  monatomic  gas  must  be  r66,  if  the  assumptions 
we  have  made  on  the  basis  of  the  kinetic  theory  are  justified. 

As  has  already  been  mentioned,  Cr  is  somewhat  difficult  to 

1  Boltzmann,  loe.  cit.,  p.  54. 


GASES  47 

determine  directly,  and  to  test  the  above  deduction  from  the 
kinetic  theory  it  is  simpler  to  determine  the  ratio  CP/CV  in- 
directly, which  can  be  done  in  various  ways,  for  example,  by 
measuring  the  velocity  of  sound  in  a  gas.  Kundt  and  Warburg 
(1876)  therefore  determined  the  velocity  of  sound  in  mercury 
vapour  and  obtained  for  the  above  ratio  the  value  r66,  in  exact 
accord  with  the  theoretical  value,  undoubtedly  one  of  the  most 
striking  triumphs  of  the  kinetic  theory. 

Conversely,  a  gas  for  which  the  ratio  CP/CV  is  i  '66  must  be 
monatomic,  and  by  this  method  Ramsay  showed  that  the  rare 
gases  argon  and  helium  are  monatomic. 

For  gases  containing  two  or  more  atoms  in  the  molecule,  the 
heat  supplied  is  employed  not  only  in  accelerating  the  rectilinear 
motion  of  the  particles,  but  also  in  performing  internal  work  in 
the  molecule.  As  the  former  effect  alone  requires  3  calories, 
the  total  molecular  heat  of  a  polyatomic  gas  will  be  3  +  a 
calories,  where  a  is  a  positive  quantity,  constant  for  any  one  gas. 
The  value  of  MQ,  will  be  5  +  a  calories,  and  the  ratio  of  the 
specific  heats  will  be 

MCP       5  +  a 

> 


less  than  1-67  but  greater  than  i. 

A  comparison  of  the  numbers  given  in  the  table  shows  that 
this  deduction  is  in  complete  accord  with  the  experimental 
facts.  It  may  be  expected  that  the  more  complex  the  molecule 
the  greater  will  be  the  amount  of  heat  expended  in  performing 
internal  work  and  therefore  the  greater  will  be  the  specific  heat. 
In  accordance  with  this,  MCB  for  i  mol  of  ether  vapour  is  33-5 
calories,  and  for  turpentine  (C10H16)  66'8  calories. 

The  specific  heat  of  monatomic  gases  is  independent  of 
temperature,  that  of  polyatomic  gases  usually  increases  slowly 
with  temperature. 

Experimental  Illustrations—  Experiments  with  gases  are 
usually  somewhat  difficult  to  perform,  and  require  special  ap- 
paratus. Experimental  illustrations  of  the  simple  gas  laws  are 


48          OUTLINES  OF  PHYSICAL  CHEMISTRY 

described  in  all  text-books  on  physics,  and  need  not  be  con- 
sidered here. 

The  determination  of  the  density l  and  hence  the  molecular 
weight  of  such  a  gas  as  carbon  dioxide  by  Regnault's  method 
may  be  performed  as  follows  :  One  of  the  bulbs  is  first  exhausted 
as  completely  as  possible  by  means  of  a  pump,  the  stop-cock 
closed,  and  the  bulb  weighed.  It  is  then  filled  with  water  by 
opening  the  stop-cock  while  the  end  of  the  tube  dips  under  the 
surface  of  water  and  again  weighed.  The  volume  of  the  bulb 
is  obtained  by  dividing  the  weight  of  the  water  by  its  density 
at  the  temperature  of  the  experiment.  The  water  is  removed 
from  the  bulb  by  means  of  a  filter-pump,  the  interior  of  the  bulb 
is  dried  (by  washing  out  with  alcohol  and  ether  and  warming), 
placed  nearly  to  the  stop-cock  in  a  bath  at  constant  temperature, 
the  end  is  then  connected  to  a  T  piece  by  means  of  rubber 
tubing ;  one  of  the  free  ends  of  the  T  piece  is  connected,  through 
a  stop-cock  or  rubber  tube  and  clip,  to  a  pump,  the  other,  also 
through  a  stop-cock  or  rubber  tube  and  clip,  to  an  apparatus 
generating  carbon  dioxide.  The  bulb  is  evacuated  by  means 
of  the  pump,  the  stop-cock  connecting  it  with  the  latter  is  then 
closed,  that  connecting  it  with  the  carbon  dioxide  apparatus 
opened,  the  bulb  filled  with  carbon  dioxide,  disconnected  and 
weighed.  As  the  apparatus  fills  it  with  carbon  dioxide  at  rather 
more  than  atmospheric  pressure,  the  stop-cock  is  opened  for  a 
moment  to  adjust  it  to  atmospheric  pressure  before  weighing. 
The  weight  of  a  known  volume  of  the  gas  at  known  temperature 
and  pressure  having  thus  been  determined,  its  density  and 
molecular  weight  can  readily  be  calculated. 

The  determination  of  vapour  densities  by  Victor  Meyer's 
method  is  fully  described  on  page  38,  and  may  readily  be 
performed  by  the  student  with  ether  or  chloroform,  steam  being 
used  as  jacketing  vapour. 

1  For  full  details  as  to  the  manipulation  of  gases,  consult  Travers' 
Experimental  Study  of  Gases  (Macmillan,  1901). 


CHAPTER  III 
LIQUIDS 

General — Liquids,  like  gases,  have  no  definite  form,  but, 
unlike  the  latter,  they  have  a  definite  volume,  which  is  only 
altered  to  a  comparatively  small  extent  by  changes  of  tempera- 
ture and  pressure. 

In  contrast  to  the  simple  gas  laws,  the  formulae  connecting 
temperature,  pressure  and  volume  of  liquids  are  very  compli- 
cated and  empirical  in  character,  and  depend  also  on  the  nature 
of  the  liquid.  This  is,  of  course,  connected  with  the  fact  that 
liquids  represent  a  much  more  condensed  form  of  matter  than 
gases.  i  c.c.  of  liquid  water  at  100°,  when  converted  into 
vapour  at  the  same  temperature,  occupies  a  volume  of  over 
1600  c.c.  It  seems  plausible  to  suggest  that  the  main  reason 
why  the  formulas  representing  the  behaviour  of  liquids  are  so 
much  more  complicated  than  the  gas  laws  is  that  the  mutual 
attraction  of  the  particles,  which  is  almost  negligible  in  the  case 
of  gases  (p.  34),  is  of  predominant  importance  for  liquids. 

As  is  well  known,  gases  can  be  liquefied  by  increasing  the 
pressure  and  lowering  the  temperature ;  and,  conversely,  by 
raising  the  temperature  and  diminishing  the  pressure  a  liquid 
can  be  changed  to  a  gas.  It  is  shown  in  the  next  section  that 
there  is  no  difference  in  kind,  but  only  a  difference  in  degree, 
between  liquids  and  gases. 

Transition  from  Gaseous  to  Liquid  State.  Critical 
Phenomena — If  gaseous  carbon  dioxide,  below  31°,  is  con- 
fined in  a  tube  and  the  pressure  on  it  gradually  increased,  a 
point  will  be  reached  at  which  liquid  makes  its  appearance  in 
4  49 


50         OUTLINES  OF  PHYSICAL  CHEMISTRY 


the  tube,  and  the  whole  of  the  gas  can  be  liquefied  without 
appreciable  increase  of  pressure.  If,  however,  carbon  dioxide 
above  31°  is  continuously  compressed,  no  separation  into  two 
layers  (liquid  and  gas)  occurs,  no  matter  how  high  the  pressure 
applied.  Similarly,  if  carbon  dioxide  is  contained  in  a  sealed 
tube,  under  such  conditions  that  both  liquid  and  gas  are 
'present,  and  the  temperature  is  gradually  raised,  it  will  be 
noticed  that  when  the  temperature  reaches  31°  the  boundary 
between  liquid  and  vapour  disappears,  and  the  contents  of  the 
tube  become  homogeneous.  Other  liquids  show 
the  same  remarkable  phenomena,  but  at  tem- 
peratures which  are  characteristic  for  each  sub- 
stance. This  temperature  is  known  as  the  critical 
temperature;  above  its  critical  temperature  no 
pressure,  however  great,  will  serve  to  liquefy  a 
gas,  below  its  critical  temperature  any  gas  can  be 
liquefied  by  pressure.  That  pressure  which  is 
just  sufficient  to  liquefy  a  gas  at  the  critical  tem- 
perature is  termed  the  critical  pressure,  and  the 
specific  volume  under  these  conditions  is  called 
the  critical  volume. 

The  critical  phenomena  may  be  observed,  and 
rough  measurements  of  the  constants  obtained, 
with  an  apparatus  (Fig.  3)  used  by  Cagniard  de 
la  Tour,  who  discovered  these  phenomena  in 
1822.  The  upper  part  of  the  branch  A  contains 
a  suitable  volume  of  the  liquid  to  be  examined, 
the  branch  B,  the  upper  pait  of  which  is  gradu- 
ated, contains  a  little  air  to  act  as  a  manometer, 
the  remainder  of  the  apparatus  (the  shaded  part 
in  the  figure)  is  filled  with  mercury.  The  tube 
at  first  contains  both  vapour  and  liquid,  but  on  gradually  raising 
the  temperature,  a  point  is  ultimately  reached  at  which  the 
boundary  between  liquid  and  vapour  becomes  faint,  and  finally 
disappears ;  the  tube  is  momentarily  filled  with  peculiar  flicker- 


FIG.  3. 


LIQUIDS  S1 

ing  striae,  and  then  the  contents  become  quite  homogeneous. 
On  allowing  to  cool,  a  mist  suddenly  appears  in  the  tube  at  a 
certain  temperature,  and  separation  into  liquid  and  vapour 
again  occurs.  The  temperature  at  which  the  boundary  dis- 
appears on  heating  or  reappears  on  cooling  approximates  to 
the  critical  temperature,  and  the  critical  pressure  can  be  cal- 
culated from  the  volume  of  air  in  B.  Accurate  measurements 
of  the  constants  may  be  made  by  methods  described  by  Young l 
and  others.  As  the  temperature  rises,  the  density  of  the  liquid 
in  the  sealed  tube  naturally  decreases,  whilst  that  of  the  vapour 
increases,  and  it  has  been  shown  that  at  the  critical  temperature 
the  densities  of  liquid  and  vapour  are  equal.  The  critical 
temperatures  and  pressures  of  a  few  substances  are  given  in 
the  accompanying  table  : — 


Critical 
Temperature,  C. 

Critical  Pressure 
(Atmospheres). 

Helium 

-  267-268° 

2'3 

Hydrogen 

-  238° 

15 

Nitrogen  . 

-  149° 

27 

Oxygen     . 

-II9° 

58 

Carbon  dioxide 

31° 

72 

Ethyl  ether 

195° 

35 

Ethyl  alcohol 

243° 

63 

Behaviour  of  Gases  on  Compression — We  have  already 
learnt  that  if  gaseous  carbon  dioxide  is  compressed  at  a  tem- 
perature below  31°  it  can  be  liquefied,  but  if  the  compression 
is  carried  out  above  31°  no  separation  into  two  layers  occurs. 
These  relations  are  best  shown  diagrammatically,  as  in  Fig.  4,  in 
which  the  ordinates  represent  the  pressures  and  the  abscissae 
the  corresponding  volumes  at  constant  temperature.  If  the 
gas  in  question  obeys  Boyle's  law,  the  curves  obtained  by 
plotting  the  pressures  against  the  corresponding  volumes  at 
constant  temperature  (the  so-called  isothermals)  are  hyperbolas, 
corresponding  with  the  equation/z;  =  constant,  and  this  condi- 
tion is  approximately  fulfilled  by  air,  as  shown  in  the  upper  right  - 

1  Phil.  Mag.,  1892,  [v.],  33,  153. 


OUTLINES  OF  PHYSICAL  CHEMISTRY 


hand  corner  of  the  diagram.  An  examination  of  the  isothermals 
for  carbon  dioxide  shows  that  the  same  is  nearly  true  of  this 
gas  at  48-1°,  but  at  35-5,  and  still  more  at  32*5,  the  isothermals 
deviate  from  those  of  an  ideal  gas.  At  the  latter  temperature 
it  is  very  interesting  to  observe  that  the  compressibility  at  75 
Y 

t 


Air. 


Carbon 


FIG.  4. 

atmospheres  is  very  great  for  a  short  part  of  the  curve,  and 
beyond  that  point  extremely  small ;  in  the  latter  respect  the 
highly  compressed  gas  resembles  a  liquid.  At  the  critical 
point,  31'!°,  the  curve  is  for  a  short  distance  practically  hori- 
zontal, thus  representing  a  great  decrease  of  volume  for  a  small 
change  of  pressure — in  other  words,  a  high  compressibility. 
Finally,  at  21-1°  and  13*1°,  separation  of  liquid  takes  place,  the 


LIQUIDS  53 

curves  run  horizontal  whilst  the  gas  is  changing  to  liquid  at 
constant  pressure,  and  then  the  curves  run  almost  vertical, 
indicating  a  small  decrease  of  volume  with  increase  of  pres- 
sure (i.e.,  a  small  compressibility),  characteristic  of  liquids.  It 
is  evident  from  the  foregoing  that  at  any  point  within  the 
dotted  line  ABC  both  vapour  and  liquid  are  present  ;  at  any 
point  outside  only  one  form  of  matter,  either  vapour  or  liquid. 

The  above  considerations  serve  to  show  that  there  is  no 
fundamental  distinction  between  gases  and  liquids  :  a  highly- 
compressed  gas  above  its  critical  point  cannot  be  definitely 
classified  either  as  liquid  or  gas.  It  is  evident  from  the  figure 
that  as  regards  compressibility,  highly  compressed  carbon  dioxide 
behaves  more  like  a  liquid  than  a  gas.  //  is,  in  fact,  possible 
to  pass  from  the  typically  liquid  to  the  gaseous  form,  and  vice 
versa,  without  a  separation  into  two  layers.  Thus  liquid  carbon 
dioxide  below  31°,  under  the  conditions  represented  by  the 
point  x-^  in  Fig.  5,  may  be  compressed  above  its  critical  pressure 
along  xlyl  and  then  warmed  above  its  critical  temperature 
whilst  the  pressure  is  kept  constant  at  y^  During  this  process 
no  separation  into  two  layers  will  be  noticed,  and  by  now  re- 
ducing the  pressure  the  fluid  can  be  obtained  in  as  dilute  a 
form  as  desired  (what  is  ordinarily  termed  a  gas),  say  the  con- 
dition represented  by  x,  whilst  remaining  quite  homogeneous. 
Similarly  a  gas  can  be  completely  converted  to  a  liquid  without 
discontinuity,  along  xyy^x^ 

Application  of  Yan  der  Waals'  Equation  to  Critical 
Phenomena  —  We  have  already  learnt  that  no  actual  gas 
follows  the  gas  laws  quite  strictly,  and,  further,  that  the 
behaviour  of  actual  gases  can  be  represented  with  fair  ac- 
curacy, even  up  to  high  pressures,  by  van  der  Waals'  equation, 


p  +  w    (v  ~  ^)  =  RT-      If  this    equation    is   arranged    in 
descending  powers  of  V  it  becomes 


54 


OUTLINES  OF  PHYSICAL  CHEMISTRY 


This  is  a  cubic  equation,  V  being  treated  as  the  variable 
and  P  and  T,  as  well  as  a,  b,  and  R,  as  constants.  Ac- 
cording to  the  values  of  these  constants  the  equation  has 
either  three  real  roots  or  one  real  and  two  imaginary  roots. 
Otherwise  expressed,  the  magnitudes  of  a  and  b  may  be  such 
that  at  one  temperature  and  pressure,  the  volume  V  has  three 
real  values,  whilst  at  another  temperature  and  pressure  it  may 

have  only  one  real 
value.  We  will  now 
compare  these  theo- 
retical deductions  with 
the  actual  case  of  car- 
bon dioxide.  It  is  clear 
from  Fig.  4  that  at 
13-1°  and  48  atmo- 
spheres, carbon  dioxide 
has  two  volumes,  as  a 
gas  (represented  by  the 
point  D)  and  as  a  liquid 
(the  point  E),  but  the 
third  volume  demanded 
by  the  equation  is  not 
shown.  At  48*  i°,  on 
the  other  hand,  there  is 
only  one  volume  for 
each  pressure,  corres- 
ponding with  one  real 
root  of  the  equation 
under  these  conditions. 


Volume' 


FIG.  5. 


Some  light  is  thrown  on  the  question  of  the  missing  third 
real  volume  when  the  isothermal  curves  for  carbon  dioxide  are 
plotted  by  substituting  the  values  of  a  and  b,  found  experi- 
mentally (p.  34)  in  equation  (i).  The  wavy  curve  ABCDE 
shown  in  Fig.  5  was  obtained  in  this  way ;  on  comparison  with 
the  experimental  curve  for  carbon  dioxide  (Fig.  4),  it  will  be 


LIQUIDS  55 

seen  that  whereas  the  points  D  and  E  in  the  latter  isothermal 
for  13°  are  joined  by  a  straight  line  DE,  in  the  former  the 
corresponding  points  E  and  A  are  joined  by  the  dotted  line 
ABCDE,  which  represents  a  change  from  the  gaseous  to  the  liquid 
form  without  discontinuity.  The  point  C,  at  which  the  line  of 
constant  pressure  cuts  the  isothermal,  represents  the  third  of 
the  volumes  required  by  the  above  cubic  equation,  but  it 
probably  cannot  be  realised  in  practice,  as  the  part  DCB  of 
the  curve  on  which  it  occurs  represents  decrease  of  volume 
with  diminishing  pressure,  quite  contrary  to  our  usual  experi- 
ence. On  the  other  hand,  the  sections  AB  and  ED  have 
a  real  meaning.  When  a  vapour  is  compressed  till  saturated, 
it  does  not  necessarily  liquefy  ;  in  the  complete  absence  of 
liquid  it  may  be  compressed  considerably  beyond  the  point 
at  which  liquefaction  occurs  in  the  presence  of  traces  of  liquid  ; 
in  other  words,  a  part  of  the  curve  ED  may  be  experimen- 
tally realised.  Similarly,  water  may  be  heated  in  a  carefully 
cleaned  vessel  several  degrees  above  its  boiling  point,  that  is, 
it  does  not  necessarily  pass  into  vapour  when  the  superincum- 
bent pressure  is  less  than  its  vapour  pressure,  and  a  part  of 
the  curve  AB  may  thus  be  experimentally  realised.  Similar 
phenomena  will  be  met  with  later  ;  it  often  happens  that  when 
a  system  is  under  such  conditions  that  the  separation  of  another 
phase  (form  of  matter)  is  possible,  the  change  does  not  occur 
in  the  absence  of  the  new  phase. 

Van  der  Waals'  equation  can  also  be  employed  to  obtain 
important  relations  between  the  critical  constants  and  the  other 
characteristic  constants  representing  the  behaviour  of  gases.  It 
has  already  been  pointed  out  that  the  densities  and  consequently 
the  volumes  of  liquid  and  gas  become  equal  at  the  critical 
temperature,  and  as  this  must  also  be  true  for  the  intermediate 
third  volume,  it  follows  that  the  three  roots  of  the  equation 


become   equal    under    these   conditions.     If,    in    this   general 


56         OUTLINES  OF  PHYSICAL  CHEMISTRY 

equation,  we  call  the  three  roots  Vv  V2  and  V8,  then  the  equation 
(V-VJfV-  V2)(V-  V3)  =  o,  must  hold,  which,  when  the  roots 
are  equal,  becomes 

(V  -  V*)3  =  Vs  -  3V*V2  +  3V*2V  -  V*3  =  o  (2), 

where  V*  is  the  critical  volume.  Equating  the  coefficients  of 
the  identical  equations  (i)  and  (2),  we  have 


...      a  ....       ab          .  ..... 

+  -pj-  =  3V*  W  ;  ^  =  3  vi  (n)  ;  p-;  =  v*  H- 

From  the  last  three  equations,  the  values  of  the  critical  con- 
stants can  readily  be  obtained  in  terms  of  R,  a  and  b.  We 
have 

Critical  volume  V^  =  3^  (from  ii  and  iii), 

Critical  pressure  P*  =  —  -=*  (from  ii), 
Critical  temperature  Tk  —  —  ^-7  (from  i). 

We  thus  reach  the  interesting  result  that  the  critical  constants 
may  be  calculated  from  the  deviations  from  the  gas  laws,  when 
the  latter  are  expressed  in  terms  of  the  constants  a  and  b  of 
Van  der  Waals'  equation.  As  an  illustration  of  the  satisfactory 
agreement  between  the  observed  and  calculated  values,  we  will 
take  the  data  for  ethylene,  for  which  a  =  0-00786,  b  =  0^0024, 
R  =  0-0037. 
Vk  =  0*0072  (observed  value  0*006), 

Ft  =  -  7—^  -  -5-  =  so'S  (observed  value  si  atmospheres) 
27  x  (0-0024)2 

T*  =  -  8  X  °'0°786  --  262°  Abs.  (observed  value  282°). 
27  x  0*0024  x  0-0037 

Law  of  Corresponding  States  —  Van  der  Waals  has  further 
pointed  out  that  if  the  pressure,  volume  and  temperature  of  a 
substance  are  expressed  as  multiples  of  the  critical  values,  that 
is,  if  we  put  P  =  aPfc,  V  =  /3V^,  T  =  yT*,  and  then  substitute 
in  the  equation  (P  +  a/V2)(V  -  b)  =  RT,  P*,  V*  and  T*  being 


LIQUIDS  57 

replaced  by  their  values  in  terms  of  a,  b  and  R,  the  equation 
simplifies  to 


This  equation  does  not  contain  anything  characteristic  of 
the  behaviour  of  an  individual  substance,  and  ought  therefore 
to  hold  for  all  substances  in  the  gaseous  and  liquid  state. 
Experiment  shows,  however,  that  it  is  only  to  be  regarded  as 
a  first  approximation,  the  deviation  in  many  cases  being  much 
greater  than  the  experimental  error. 

For  our  present  purpose,  these  considerations  are  chiefly  of 
importance  as  affording  information  regarding  the  proper  con- 
ditions for  comparison  of  the  physical  properties  of  liquids.  If 
we  wish,  for  example,  to  compare  the  molecular  volumes  of 
ether  and  benzene,  it  would  probably  not  be  satisfactory  to 
compare  them  at  the  ordinary  temperature  of  a  room,  as  this 
would  be  near  the  boiling-point  of  ether,  35°,  but  much  below 
that  of  alcohol,  78°.  According  to  van  der  Waals,  the  proper 
temperatures  for  comparison,  the  so-called  "  corresponding  tem- 
peratures," are  those  which  are  equal  fractions  of  the  respective 
critical  temperatures.  Thus,  if  we  choose  20°,  or  293°  Abs., 
as  the  temperature  of  experiment  for  ether,  the  critical  tem- 
perature of  which  is  195°,  or  468°  Abs.,  the  proper  temperature, 
/,  for  comparison  with  alcohol  (critical  temperature,  243°  C.) 

will  be  given  by   273J"g2°  =  ^g  *»  whence  /=5l0-     The 

same  considerations  apply  to  the  pressures. 

The  theoretical  basis  for  this  method  of  comparison  is  that, 
as  mentioned  above,  the  choosing  of  pressures,  volumes  or  tem- 
peratures which  for  different  substances  bear  the  same  proportion 
to  their  respective  critical  constants  leads,  when  substituted  in 
van  der  Waals'  equation,  to  an  equation  which  is  the  same  for 
all  substances,  and  the  practical  justification  for  choosing  these 
as  corresponding  conditions  is  that  more  regularities  are  actually 


58          OUTLINES  OF  PHYSICAL  CHEMISTRY 

observed  by  this  method  than  when  the  comparison  is  made 
under  other  circumstances. 

Liquefaction  of  Gases— As  already  indicated,  all  gases 
can  be  liquefied  by  cooling  them  below  their  respective  critical 
temperatures  and  applying  pressure.  The  methods  employed 
for  this  purpose  by  Cailletet,  Pictet,  Wroblewski  and  others 
are  fully  described  in  text-books  of  physics.  In  recent  years 
the  older  methods  have  been  almost  completely  displaced,  in 
the  case  of  the  less  condensible  gases,  such  as  air  and  hydro- 
gen, by  a  method  introduced  almost  simultaneously  by  Linde 
and  by  Hampson.  The  principle  of  the  method  is  that  when  a 
gas  is  allowed  to  pass  from  a  high  to  a  low  pressure  through  a 
porous  plug  without  performing  external  work  it  becomes  cooled 
(Joule-Thomson  effect).  The  cooling  effect  is  due  to  the 
performance  of  internal  work  in  overcoming  the  mutual  attrac- 
tion of  the  particles,  and  is  therefore  only  observed  for  "  im- 
perfect "  gases  (p.  34).  The  effect  is  the  greater  the  lower 
the  temperature  at  which  the  expansion  takes  place,  and  the 
greater  the  difference  of  pressure  on  the  two  sides  of  the  plug. 
The  cooling  effects  thus  obtained  are  summed  up  in  a  very 
ingenious  way  by  the  principle  of  "  contrary  currents,"  the  same 
quantity  of  gas  being  made  to  circulate  through  the  apparatus 
several  times,  and  after  passing  through  the  plug  being  caused 
to  flow  over  and  cool  the  tube  through  which  a  further  quantity 
of  gas  is  passing  on  its  way  to  the  plug  (or  small  orifice). 

The  apparatus  employed  is  represented  diagrammatically  in 
Fig.  6.  By  means  of  the  pump  A,  the  gas  is  compressed  in 
B  to  (say)  100  atmospheres,  the  heat  given  out  in  this  process 
being  absorbed  by  surrounding  B  with  a  vessel  through  which 
a  continuous  current  of  cold  water  is  passed.  The  cooled,  com- 
pressed gas  then  passes  down  the  central  tube  G,  towards  the 
plug  E,  being  further  cooled  on  the  way  by  the  gas  passing  up 
the  wide  tube  D,  which  has  just  expanded  through  the  plug. 
After  passing  through  E  and  thus  falling  to  its  original  pressure, 
the  gas  passes  upwards  over  the  central  tube  G  and  again 


LIQUIDS 


59 


B 


reaches  A  by  the  tube  C  and  the  left-hand  valve  at  the  bottom 
of  A.  The  direction  of  the  circulating  stream  of  gas  is  indicated 
by  the  arrows.  In  course  of  time,  the  temperature  becomes  so 
low  that  part  of  the  gas  is  liquefied 
and  collects  in  the  vessel  F. 
More  air  is  drawn  into  the  appar- 
atus as  required,  and  the  process 
is  continuous. 

By  means  of  an  apparatus  con- 
structed on  this  principle  Dewar, 
and,  somewhat  later,  Travers, 
succeeded  in  obtaining  liquid 
hydrogen  in  quantity.  All  known 
gases  have  now  been  liquefied. 
The  liquefaction  of  helium  was 
effected  quite  recently  by  Kam- 
merlingh  Onnes. 


RELATION  BETWEEN  PHYSI- 
CAL PROPERTIES  AND 
CHEMICAL  CONSTITUTION 

General  —  The  foregoing  para- 
graphs of  this  chapter  represent 
an  introduction  to  the  relation- 
ship between  the  physical  pro- 
perties of  liquids  and  their  chemi- 
cal composition,  inasmuch  as  in- 
formation has  been  gained  as 
to  the  conditions  under  which 
measurements  should  be  made 
with  different  liquids  in  order  to 
obtain  comparable  results  (theory 


FlG- 


of  corresponding  states).  Although  in  this  chapter  we  are 
mainly  concerned  with  the  physical  properties  of  pure  liquids, 
it  is  convenient  to  include  also  some  observations  with  solu- 


60          OUTLINES  OF  PHYSICAL  CHEMISTRY 

tions.  We  will  deal  shortly  with  the  following  physical  pro- 
perties: (i)  Atomic  and  molecular  volumes;  (2)  refractivity ; 
(3)  rotation  of  plane  of  polarization  of  light ;  (4)  absorption 
of  light ;  (5)  viscosity. 

Atomic  and  Molecular  Volumes — In  the  case  of  gases, 
we  have  seen  that  simple  relations  are  obtained  when  the 
volumes  occupied  by  different  substances  in  the  ratio  of  their 
molecular  weights  are  compared ;  at  the  same  temperature  and 
pressure,  the  volumes  are  equal.  The  justification  for  taking 
the  molecular  weights  (in  grams,  for  instance)  as  comparable 
quantities  is  that,  according  to  the  molecular  theory,  equal 
numbers  of  molecules  of  different  substances  are  thus  compared. 
Similarly,  in  dealing  with  liquids,  it  is  usual  to  determine  the 
molecular  volume  of  the  liquid,  i.e.,  the  volume  occupied  by  the 
molecular  weight  of  the  liquid  in  grams,  which  is,  of  course,  ob- 
tained by  dividing  the  molecular  weight  in  grams  by  the  density 
of  the  liquid  at  the  temperature  of  experiment.  As  the  specific 
volume,  v,  of  a  liquid  is  inversely  as  the  density,  the  molecular 
volume  may  also  be  defined  as  molecular  weight  in  grams  x 
sp.  volume.  Similarly,  the  atomic  volume  =  (atomic  weight  in 
grams)  -f-  density,  or,  (atomic  weight  in  grams)  x  sp.  volume. 

Kopp  was  the  first  chemist  to  carry  out  an  extended  series  of 
observations  on  this  subject,  and  he  found  that  the  most  regular 
results  were  obtained  when  molecular  volumes  were  determined, 
not  at  the  same  temperature,  but  at  the  boiling-points  of  the 
respective  liquids  under  atmospheric  pressure.  It  is  interesting 
to  observe  that  this  purely  empirical  method  of  procedure  was 
found  much  later  to  be  theoretically  justifiable,  as  the  boiling- 
points  of  most  liquids  are  approximately  two-thirds  of  their 
respective  critical  temperatures  (both  measured  on  the  absolute 
scale).  The  boiling-points  are  therefore  corresponding  tempera- 
tures, (p.  57). 

Kopp  found  that  as  a  first  approximation  the  molecular 
volume  could  be  regarded  as  the  sum  of  numbers  representing 


LIQUIDS  6 1 

the  volumes  of  the  component  atoms.  The  atomic  volumes  of 
the  commoner  elements  occurring  in  organic  compounds  are  as 
follows  : — 

C         H          Cl          Br         I  S        0(0 -H)  0(0  =  ) 

ii       5*5       22'8       27*8     37-5       22*6          7*8          12*2 

In  some  cases  the  atomic  volume  depends  on  the  way  in  which 
the  element  is  bound,  thus  oxygen  joined  to  hydrogen  (hydroxyl 
oxygen)  has  the  atomic  volume  7*8,  whilst  for  oxygen  doubly 
linked  to  carbon  (carbonyl  oxygen)  the  volume  is  i2'2.  As  an 
illustration  the  calculated  and  observed  volumes  of  acetic  acid 
may  be  compared  as  follows  : — 

2C   =    22 

4.H  «=  22 

(Carbonyl)  O  =  12-2 
(Hydroxyl)  Q  =     7 '8 

64*0 

As  the  molecular  weight  of  acetic  acid  is  60  and  its  density  at 
the  boiling-point  is  0*942  the  observed  molecular  volume  M/*/ 
=  63-7. 

It  should  be  mentioned  that  the  atomic  volumes  given 
above  are  not  obtained  directly,  but  by  comparison  of  chemical 
compounds  with  definite  differences  of  composition  (e.g.t  the 
difference  in  the  molecular  volumes  of  the  compounds  C4H10 
and  C4H8  gives  the  volume  of  two  atoms  of  hydrogen),  and  are 
therefore  not  necessarily  the  same  as  those  for  the  free  elements. 
In  some  cases,  however,  the  two  values  coincide,  thus  the  atomic 
volumes  of  the  free  halogens,  chlorine  and  bromine,  at  their  boil- 
ing-points are  23-5  and  27*1  respectively,  whilst  their  values  in 
combination  are  22-8  and  27-8,  so  that  the  halogens  have  ap- 
proximately the  same  volume  in  the  free  and  combined  condi- 
tion. The  same  is  approximately  true  for  certain  other  elements 
for  which  comparison  is  possible. 

The  extended  investigations  of  Thorpe,  Lessen  and  Schiff 


62          OUTLINES  OF  PHYSICAL  CHEMISTRY 

afford  a  general  confirmation  of  Kopp's  conclusions  ;  the  cal- 
culated and  observed  values  generally  agree  within  about  4  per 
cent. 

Although,  strictly  speaking,  the  consideration  of  the  mole- 
cular volume  of  a  substance  in  solution  does  not  belong  to  this 
section,  it  is  convenient  to  refer  to  it  here.  The  molecular  solu- 
tion volume^  Mz;,  of  a  substance  may  readily  be  calculated  from  the 

formula  Mv  =  — -5 -^r,  where  M  is  the  molecular  weight 

of  the  solute  in  grams,  n  the  weight  of  the  solvent  containing  M 
grams  of- solute,  ^'the  density  of  the  solution,  and  d'  that  of  the 
solvent.  This  formula  is  derived  on  the  assumption,  which  is 
certainly  not  justifiable,  that  the  density  of  the  solvent  itself  is 
not  affected  by  dissolving  a  substance  in  it,  and  therefore  M#is 
only  the  "  apparent "  solution  volume.  The  molecular  volume 
is  sometimes  nearly  the  same  in  the  free  state  and  in  solution1 
(e.g.,  bromine  in  carbon  tetrachloride),  but  is  often  much  less 
(e.g.,  many  salts  in  water). 

Additive,  Constitutive  and  Colligative  Properties — 
The  molecular  volume  is  a  good  example  of  what  is  termed 
an  additive  property,  since  it  can  be  represented  as  the  sum  of 
volumes  pertaining  to  the  component  atoms.  It  is  not,  how- 
ever, strictly  additive,  since  it  is  influenced  somewhat  by  the 
arrangement  of  the  atoms  in  the  molecule,  and  therefore  the 
atoms  to  some  extent  influence  each  other.  Properties  which 
depend  largely  on  the  constitution  of  the  molecule,  in  other 
words,  on  the  arrangement  of  the  atoms  in  the  molecule,  are 
termed  constitutive ;  a  typical  constitutive  property  is  the  rota- 
tion of  the  plane  of  polarization  of  light  (p.  66).  The  only 
strictly  additive  property  is  weight.  Other  properties,  such  as 
the  refractivity,  the  molecular  volume,  heat  of  combustion,  etc., 
are  more  or  less  additive,  but  are  to  some  extent  complicated 
by  constitutive  influences,  probably  due  largely  to  the  mutual 
influence  of  the  atoms. 

There  is  a  third  class  of  properties,  which  always  retain  the 

1Lumsden,  Trans.  Chem.  Soc.,  1907,  91,  24;  Dawson,  ibid.,  1910,  97, 
1041. 


LIQUIDS  63 

same  value  independent  of  the  number  and  nature  of  the  atoms 
in  a  molecule  or  of  their  arrangement,  and  depend  only  on  the 
number  of  molecules.  A  good  illustration  of  these  properties 
has  already  been  met  with  in  connection  with  gases.  When  these 
are  taken  in  quantities  which,  according  to  the  atomic  theory,  are 
proportional  to  their  molecular  weights,  they  all  exert  the  same 
pressure  when  occupying  equal  volumes  at  the  same  tempera- 
ture. Such  properties  have  been  termed  colligative  by  Ostwald. 

Many  illustrations  of  these  three  classes  of  properties  will  be 
met  with  in  the  course  of  our  work. 

Refractivity — The  velocity  with  which  light  is  propagated 
through  different  substances  is  very  different.      The  relative 
velocities  in  two  media  can  be 
deduced  when  the  change  in 

direction  of  a  ray  of  light  in  I          * 

passing  from  one  medium  to     ^^  ' 

another  is  known.  When  the 
ray  passes  from  one  medium  to 
the  other,  the  incident  ray,  the 

J  '  —     _____   i   11 _  — _    __ 

refracted    ray   (in   the  second         rz  E.  I  i:  V-E.r¥jL~-Irr~_.-- ~ 
medium)  and    the   normal    to  -  j- 1"^  _~_~T~J^i."-: 

the  boundary  between  the  two 
media  (a  line  drawn  perpen.  FIG.  7. 

dicular  to  the  boundary  where 

the  incident  ray  meets  it)  are  in  one  plane.  If  /  is  the  angle  of 
incidence  (the  angle  between  the  incident  ray  and  the  normal) 
(Fig.  7)  and  r  is  the  angle  of  refraction  (the  angle  between  the 
normal  and  the  refracted  ray)  and  7^  and  v^  the  respective  velo- 
cities of  light  in  the  two  media,  it  can  be  shown  that  the  ratio  of 
the  sine  of  the  angle  of  incidence  to  the  sine  of  the  angle  of 
refraction  is  constant,  and  is  equal  to  the  ratio  of  the  velocity 
of  light  in  the  two  media.  The  ratio  in  question  is  termed  the 
index  of  refraction,  and  is  usually  represented  by  the  symbol  n. 

We  have  therefore  the  relation  n  =  — —  =  -i. 

sin  r      vn 


64          OUTLINES  OF  PHYSICAL  CHEMISTRY 

If  the  first  medium  is  a  vacuum,  n  is  always  greater  than  i 
— in  other  words,  light  attains  its  greatest  velocity  in  a  vacuum, 
and  is  retarded  on  passing  through  matter.  The  refractive 
index  is,  however,  often  referred  to  air  as  unity,  and  to  convert 
the  values  thus  found  to  a  vacuum  they  must  be  multiplied  by 
1*00029,  giving  what  is  termed  the  "absolute  refractive  index". 

An  instrument  employed  for  the  determination  of  refractive 
indices  is  termed  a  refractometer.  Among  the  more  convenient 
forms  of  refractometer,  those  due  to  Abbe  and  to  Pulfrich  may 
be  specially  mentioned. 

Ordinary  white  light  cannot  be  employed  for  refractivity 
measurements,  as  the  component  rays  are  refracted  or  retarded 
to  a  different  extent  on  passing  through  matter,  the  rays  thus 
scattered  or  dispersed  giving  rise  to  a  spectrum.  This  difficulty 
is  avoided  by  using  light  of  the  same  wave-length  (so-called 
monochromatic  light),  and  for  this  purpose  sodium  light,  the 
wave-length  of  which  is  represented  by  the  letter  D,  is  con- 
venient. Measurements  of  the  refractive  index  referred  to 
sodium  light  are  represented  by  the  symbol  «D. 

The  refractive  index  of  a  given  substance,  like  any  other 
property,  depends  on  the  conditions  of  temperature,  pressure, 
etc.,  under  which  the  measurements  are  made.  It  has  been 
found  convenient  to  express  the  results  of  measurements  not 

simply  in  terms   of   nD,  but  in  terms   of  the  function  -— - — 

where  d  is  the  density  of  the  liquid  or  gas  (Gladstone  and 
Dale,  1858).  This  purely  empirical  function,  known  as  the 
refraction  constant,1  is,  for  any  given  substance,  practically  inde- 
pendent of  the  temperature.  In  1880,  Lorenz  and  Lorentz 
arrived  simultaneously,  from  theoretical  considerations,  at  the 

somewhat  more  complicated  expression,  —^ .  — ,  and  showed 

that,  for  the  same  substance,  it  remained  fairly  constant,  not 
only  for  widely  differing  temperatures,  but  even  for  the  change 
from  liquid  to  gaseous  form.  Thus  Eykman  found  that  the 

1  The  expression  here  called  the  "  refraction  constant  "  is  sometimes 
called  the  "  specific  refractivity". 


LIQUIDS  65 

value  of  this  function  for  isosafrol,  C10H10O2,  amounted  to 
0-2925  and  0-2962  at  17-6°  and  141°  respectively,  and  Lorenz 
obtained  for  water  at  10°  and  water  vapour  at  100°  the  values 
0*2068  and  0*2061  respectively. 

For  comparative  purposes,  it  is  usual  to  employ  the  atomic 
refraction  (atomic  weight  x  refraction  constant)  and  the  mole- 
cular refraction  (molecular  weight  x  refraction  constant) ;  the 
latter,  if  we  employ  the  second  form  of  the  refraction  constant, 

is  given  by  ~$TT —  *   ~7 »  where  M  is   the  molecular  weight. 

In  this  case  also  it  has  been  found,  from  measurements  on 
many  organic  liquids,  that  the  molecular  refraction  may  be 
represented  to  a  first  approximation  as  the  sum  of  the  refrac- 
tions of  the  component  atoms,  so  that  the  refractive  power  is 
largely  an  additive  property. 

Just  as  in  the  case  of  molecular  volumes,  however,  there  are 
certain  deviations  from  this  additive  behaviour  (constitutive 
influences)  which  may  be  connected  with  the  arrangement  of 
the  atoms  in  the  molecule.  Briihl,1  who  has  been  particularly 
prominent  in  investigating  this  question,  points  out  that  the 
molecular  refraction  of  compounds  containing  double  and  triple 
bonds  is  greater  than  the  calculated  value,  and  he  takes  account 
of  this  constitutive  influence  by  ascribing  definite  refractivities 
to  these  bonds.  The  most  recent  values  for  a  few  of  the 
elements  are  as  follows  : — 

Oxygen  Double  Triple 

C  H  (in  CO  group)  (in  ethers)  (in  OH  group)  Cl  I  bond  bond 
2-418 i-ioo  2-211  1-643  1-525  5*967 13-90  1-733  2-398 

Later  investigations  show  that  neighbouring  double  or  triple 
bonds  exert  a  mutual  influence,  so  that  the  matter  becomes 
somewhat  complicated. 

Conversely,  it  is  sometimes  possible,  from  measurements^of 
the  refractive  index  (or  other  physical  property),  to  draw  con- 
clusions as  to  the  constitution  of  chemical  compounds,  but  as 

1  For  a  short  summary  of  Bruhl's  work,  by  himself,  see  Proc.  Royal 
Institution,  1906,  18,  122. 

2  The  numbers  are  referred  to  the  D  line  (sodium  light)  and  are  calcu- 
lated according  to  the  Lorentz  formula. 

5 


66          OUTLINES  OF  PHYSICAL  CHEMISTRY 

our  knowledge  of  the  relations  between  physical  properties  and 
chemical  constitution  is  very  imperfect,  this  method  should  only 
be  employed  with  great  caution.  It  is  evident  that  no  conclu- 
sions as  to  chemical  constitution  can  be  drawn  from  additive 
properties,  but  only  from  constitutive  properties. 

Rotation  of  Plane  of  Polarization  of  Light— The  pro- 
perties of  liquids  so  far  dealt  with  have  been  mainly  additive, 
the  magnitude  of  properties  such  as  volume,  effect  on  the 
speed  of  light,  etc.,  being  much  the  same  in  the  free  state  and 
in  combination.  We  have  now  to  deal  with  the  property  pos- 
sessed by  a  few  liquids  (and  dissolved  substances)  of  rotating 
the  plane  of  polarized  light — a  property  which  depends  entirely 
upon  the  arrangement  of  the  atoms  in  the  molecule.  Isomeric 
substances  have  in  general  nearly  equal  molecular  refractivity 
and  molecular  volume,  but  it  often  happens  that  of  two  isomeric 
substances,  such  as  the  two  lactic  acids,  one  rotates  the  plane 
of  polarized  light  and  the  other  does  not. 

Plane  polarized  light  (light  in  which  the  vibrations  are  all  in 
one  plane)  is  obtained  by  passing  monochromatic  light  through 
a  polarizing  prism  (Nicol  prism  or  tourmaline  plate)  which  cuts 
off  all  the  rays  except  those  vibrating  in  one  plane.  A  prism 
of  this  type  is  mounted  at  some  distance  from  another  similar 
prism  in  such  a  way  that  light  which  has  been  polarized  in  the 
first  prism  may  be  examined  after  it  has  passed  through  the 
second  prism,  which  is  termed  the  analyser.  If  now  the 
analyser  is  rotated  until  it  is  perpendicular  to  the  polarizer,  all 
the  light  which  passes  through  the  former  will  be  cut  off  by  the 
analyser,  and  on  looking  through  the  eyepiece  the  field  will 
appear  dark.  If  now,  while  the  prisms  are  in  this  relative  posi- 
tion, a  tube  filled  with  turpentine  is  placed  between  them,  the 
field  again  appears  clear,  but  becomes  dark  on  rotating  the 
analyser  through  a  certain  angle.  This  observation  is  readily 
accounted  for  on  the  view  that  the  plane  of  polarization  is 
twisted  through  a  certain  angle  whilst  the  light  is  traversing  the 
turpentine,  and  the  analyser  must  therefore  be  rotated  in  order 


LIQUIDS  67 

to  bring  it  into  the  former  relative  position  with  regard  to  the 
polarized  ray.  The  angle  through  which  the  analyser  has  been 
turned  is  read  off  on  a  graduated  scale.  The  instrument  used 
for  measuring  the  rotation  of  liquids,  which  consists  essentially 
of  the  two  prisms  and  graduated  scale,  as  described  above,  is 
termed  a  polarimeter.  The  observed  angle  of  rotation  depends 
on  the  nature  of  the  liquid,  on  the  wave-length  of  the  light 
employed  in  the  measurements,  and  on  the  temperature,  and 
is  proportional  to  the  length  of  liquid  traversed.  For  purposes 
of  comparison,  the  results  are  usually  expressed  in  terms  of  the 
specific  rotation  [a]  for  a  fixed  temperature  t  and  a  particular 
wave-length  of  light  (for  example,  sodium  light)  by  means  of 
the  formula 

•}  a 

LaJD  ==  7# 

where  a  is  the  observed  angle,  /  is  the  length  of  the  column 
of  liquid  in  decimetres,  and  d  is  the  density  of  the  liquid  at  the 
temperature  /.  The  molecular  rotation  m[a\  is  obtained  by 
multiplying  the  specific  rotation  by  the  molecular  weight  of  the 
liquid. 

The  specific  rotation  of  substances  in  solution  is  represented 
by  the  analogous  formula 

r  J.          looo. 

where  g  is  the  number  of  grams  of  solute  in  100  grams  of  the 
solution,  d  is  the  density  of  the  solution  at  the  temperature  /, 
and  a  and  /  have  the  same  significance  as  before. 

The  liquids  and  dissolved  substances  which  possess  this  re- 
markable property  are  almost  exclusively  compounds  containing 
carbon.  Further,  only  compounds  containing  an  asymmetric 
carbon  atom,  that  is,  a  carbon  atom  joined  to  four  different 
groups,  have  the  power  of  rotating  polarized  light  ( van't  Hoff  and 
Le  Bel,  1874).  For  example,  the  graphic  formula  of  ordinary 
lactic  acid,  which  is  optically  active,  may  be  written  as 
follows  : — 


68          OUTLINES  OF  PHYSICAL  CHEMISTRY 

CH3 
H— C— OH 


COOH 


showing  that  no  two  of  the  groups  attached  to  the  central 
carbon  atom  are  identical.  A  further  remarkable  fact  is  that 
when  one  form  of  a  substance,  such  as  lactic  acid,  can  rotate 
the  plane  of  polarized  light  to  the  right,  a  second  modifica- 
tion can  always  be  obtained  which,  although  identical  with 
the  first  in  all  other  physical  properties,  rotates  polarized  light 
to  the  left  to  the  same  extent  as  the  first  modification  rotates 
it  to  the  right.  The  first  is  termed  the  dextro  or  d  modi- 
fication, the  second  the  laevo  or  /  modification.  Van't  Hoff 
and  Le  Bel  account  for  this  on  the  hypothesis  that  the  four 
different  groups  are  not  in  the  same  plane  as  the  carbon 
atom,  but  are  arranged  in  the  form  of  a  tetrahedron  with 
the  carbon  atom  in  the  centre.  It  can  be  shown,  most 
readily  by  means  of  a  model,1  that  when  all  four  groups 
are  different  there  are  two  arrangements  which  cannot  be 
made  to  coincide  by  rotating  one  of  the  models.  These 
two  arrangements  behave  to  each  other  as  object  and  mirror 
image,  or  a  right-  and  left-hand  glove,  which  cannot  be 
brought  into  the  same  rektive  position,  and,  according  to  the 
theory,  correspond  with  the  dextro  and  laevo  modifications 
respectively.  If  any  two  of  the  groups  become  identical, 
however,  the  two  arrangements  can  always  be  brought  to 
coincidence,  and  there  is  no  possibility  of  optical  isomerism. 
In  calculating  the  specific  rotation  of  a  dissolved  substance, 
it  is  implicitly  assumed  that  it  is  not  affected  by  an  indifferent 
solvent.  As  a  matter  of  fact,  however,  the  molecular  rotation 
of  a  dissolved  substance  often  differs  considerably  from  its  value 

1  Models  for  this  purpose  can  be  bought  for  a  few  pence,  or  can  be  made 
by  the  student  with  a  piece  of  cork  and  four  pins  provided  with  differently 
coloured  balls  at  the  ends. 


LIQUIDS  69 

in  the  pure  state.  This  is  well  shown  by  the  following  results 
obtained  by  Patterson1  for  /-menthyl-^-tartrate  in  the  pure  state, 
and  in  1-2  per  cent,  solution. 

Molecular  Rotation  of  /-menthyW-tartrate. 

Solvent.  Molecular  Rotation  at  20°. 
None  -  284° 

Ethyl  alcohol  -306-2° 

Benzene  -  296*1° 

Nitrobenzene  -245-3° 

So  far,  no  definite  connection  has  been  found  between  any 
other  property  of  the  solvent  and  its  effect  on  the  rotation  of  a 
solute.  Almost  the  only  regularity  which  has  yet  been  dis- 
covered in  this  branch  of  the  subject  is  that  the  rotatory  power 
of  the  salt  of  an  optically  active  acid  (or  base)  in  dilute  solution 
is  independent  of  the  nature  of  the  base  (or  acid)  with  which  it 
is  combined.  This  important  result  is  further  referred  to  at  a 
later  stage. 

All  transparent  substances,  when  placed  in  a  magnetic  field, 
rotate  the  plane  of  polarized  light,  and  the  late  Sir  William 
Perkin,  who  devoted  many  years  to  the  systematic  investigation 
of  this  subject,  showed  that  this  magnetic  rotation  is,  like  refrac- 
tivity,  largely  an  additive  property. 

Absorption  of  Light 2 — When  a  ray  of  white  light  passes 
through  matter  a  greater  or  less  amount  of  absorption  invari- 
ably occurs,  and  the  spectrum  of  the  issuing  ray  shows 
dark  bands  corresponding  with  the  rays  which  have  been 
absorbed.  This  spectrum  is  termed  an  absorption  spectrum. 
Absorption  may  be  general  or  selective.  In  the  former  case 
there  is  a  general  weakening  throughout  whole  regions  of  the 
spectrum ;  in  the  latter  case,  there  are  independent  relatively 
narrow  bands  in  different  regions  of  the  spectrum. 

iSee  Trans.  Chem.  Soc.,  1905,  87,  128. 

2  Smiles,  Chemical  Constitution  and  some  Physical  Properties  (Long- 
mans, 1910),  pp.  324-423. 


70         OUTLINES  OF  PHYSICAL  CHEMISTRY 

The  absorption  spectrum  is  one  of  the  most  characteristic 
properties  of  a  given  substance  or  class  of  substances  under 
definite  conditions.  Thus,  for  instance,  the  absorption  spectra 
of  permanganates  in  dilute  solution  are  characterised  by  the 
presence  of  five  dark  bands  in  the  green. 

In  the  case  of  liquids  or  solutions,  absorption  is  most 
conveniently  measured  in  the  transmitted  light,  as  already 
indicated.  In  the  case  of  solids,  however,  observations  may  be 
made  with  reflected  light,  as  part  at  least  of  the  reflection  takes 
place  from  layers  a  little  below  the  surface,  and  the  short  distance 
traversed  is  usually  sufficient  to  produce  some  absorption. 

The  method  which  is  most  largely  employed  in  the  case  of 
liquids  is  to  use  as  a  source  of  illumination  the  electric  arc 
or  spark  passing  between  metallic  (preferably  iron)  poles,  the 
spectrum  of  the  light  being  photographed  after  the  latter  has 
passed  through  the  liquid.  Substances  which  have  high  ab- 
sorbing power  are  usually  examined  in  solution,  and  the  solvent 
chosen  should  not  itself  show  absorption  in  the  part  of  the 
spectrum  studied.  Ethyl  alcohol  is  most  largely  used  as  solvent. 

A  very  important  question  in  such  measurements  is  the 
effect  of  dilution  on  the  persistence  and  intensity  of  a  band — 
it  very  often  happens  that  a  band  appears  only  within  certain 
limits  of  dilution.  For  this  reason,  it  is  usual  to  carry  out 
measurements  with  varying  thicknesses  of  the  absorbing  layer 
and  with  varying  concentrations.  The  solutions  are.  made 
more  and  more  dilute  till  absorption  is  no  longer  observed. 
For  purposes  of  comparison,  the  solutions  to  be  examined  are 
usually  made  up  to  contain  simple  fractions  of  a  mol  per  litre. 

The  method  usually  employed  in  representing  the  results 
graphically  requires  some  explanation.  It  is  illustrated  in  Fig. 
8,  which  shows  the  absorption  in  the  ultra-violet  region  of  a 
solution  of  the  amino  derivative  of  dimethyldihydroresorcin 
in  ethyl  alcohol.  The  diagram  shows  the  presence  of  one 
band.  The  principle  of  the  method  is  that  the  oscillation 
frequencies  of  the  limits  of  the  absorption  band  are  plotted 


LIQUIDS 


2  24 


8 


against  the  logarithms  of  the  relative  thicknesses  referred  to 
the  thinnest  layer  of  the  most  dilute  solution  examined.     It  is 

more  convenient  to  use 
Oscillation  Frequencies. 

the    logarithms    of   the 

relative  thicknesses  than 
the  thicknesses  them- 
selves as  ordinates.  The 

latter  are  shown  on  the 
1.500 
1000 


500 
400 

250 
200 

100 
50 

30 

20 
15 
10 

5 

3 
2 
I 

0-6 


right-hand  side  of  the 
c  figure,  and  it  is  evident 
M  that  if  equal  increments 
o  of  thickness  were  used, 

in 

o  the  curve  would  become 

2  inconveniently  long. 
f  The   space    above    the 
5  curve   shows   the   wave 
g  lengths     of     the     light 
g  absorbed     at     different 
S  dilutions,  and  the  curve 
ft  itself     represents      the 
ft  limits  of  the  absorption. 

The  lowest  part  of  the 

3  curve,  usually  termed  the 
£    "  head,"  is  that  point  at 
§    which  the  strongest  ab- 
52    sorption  takes  place ;  in 

oc   2 1 — I IV  I  /I 1 1 1  ^    the  diagram  it  occurs  at 

an  oscillation  frequency 
of  3600  units.  The  so- 
called  "  persistence  "  of 
the  band  is  the  difference 
of  the  logarithms  of  the 
thicknesses  at  which  the  band  makes  its  appearance  and  dis- 
appears respectively,  and  is  indicated  on  the  diagram  by  its 
depth  (in  the  present  case  extending  from  i  to  23  units). 


72          OUTLINES  OF  PHYSICAL  CHEMISTRY 

It  may  be  mentioned  that  most  of  the  measurements  have 
been  made  in  the  ultra-violet  region  of  the  spectrum,  but  a 
certain  number  of  observations  have  also  been  made  in  the 
visible  and  ultra-red  regions. 

A  great  deal  of  discussion  has  taken  place  as  to  the 
mechanism  of  light  absorption,  and  a  dynamical  explanation 
has  found  most  favour.  According  to  Drude,  absorption  in  the 
ultra-violet  and  visible  regions  is  connected  with  the  presence 
of  negative  electrons  (valency  electrons),  and  there  is  doubtless 
some  intimate  connection  between  the  rate  of  vibration  of  the 
electrons  and  the  frequency  of  the  light  waves  absorbed.  It 
appears,  however,  that  absorption  in  the  ultra-red  region  is  due, 
not  to  electrons,  but  to  particles  of  much  greater  magnitude, 
probably  atoms  or  even  groups  of  atoms. 

As  already  indicated,  the  absorption  spectra  of  chemical 
compounds  are  closely  related  to  their  constitution,  and  in 
recent  years  this  method  of  elucidating  chemical  constitution 
has  come  increasingly  into  use.  The  progress  made  in  this 
branch  of  investigation  is  mainly  due  to  Hartley,  and  within 
the  last  few  years  to  Baly  and  his  co-workers.1  It  is  impossible 
here  to  do  more  than  to  indicate  in  the  briefest  way  the  broad 
differences  between  the  absorption  spectra  of  the  main  groups 
of  organic  compounds. 

According  to  Hartley,2  all  compounds  which  exert  selective 
absorption  are  of  aromatic  character,  for  example,  benzene, 
pyridine,  and  their  derivatives.  Those  showing  strong  general 
absorption  have  also  a  cyclic  structure,  but  are  not  typical  aro- 
matic compounds ;  examples,  thiophene,  piperidine,  etc.  Finally, 
compounds  which  exert  only  a  weak  general  absorption  are 
open  chain  compounds ;  examples,  fatty  alcohols,  esters,  etc. 
Although  recent  investigation  has  led  to  the  discovery  of  one 
or  two  exceptions  to  these  generalisations,  they  remain  sub- 
stantially accurate. 

Apart  from  these  broad  differences  in  the  absorption  curves 

1  Trans.  Chem.  Soc.  from  1904  onwards. 

2  British  Association  Report,  1903. 


LIQUIDS  73 

of  different  groups  of  organic  compounds,  it  has  been  shown 
by  Hartley  that  substances  of  closely  allied  constitution  have 
absorption  curves  of  similar  type.  The  recent  progress  in  the 
establishment  of  the  chemical  constitution  of  organic  compounds 
from  measurements  of  their  absorption  spectra  is  entirely  due 
to  the  application  of  this  important  rule.  Thus  if  the  con- 
stitution of  one  compound  is  known  with  certainty  from  its 
chemical  behaviour,  and  a  second  compound  can  be  represented 
by  alternative  formulae,  of  which  one  is  analogous  to  that  of 
the  compound  of  known  constitution,  a  comparison  of  absorp- 
tion spectra  often  enables  a  decision  to  be  made. 

Like  the  other  physical  methods  of  determining  chemical 
constitution,  the  one  under  discussion  should  be  used  with 
considerable  caution  in  the  present  very  imperfect  state  of  our 
knowledge  of  absorption  phenomena.  As  a  supplement  to 
purely  chemical  methods  of  determining  constitution,  however, 
especially  when  such  methods  lead  to  contradictory  results,  it 
is  rendering  valuable  service. 

As  regards  the  additive  character  of  absorption  spectra, 
comparatively  little  is  known  with  certainty.  The  determina- 
tion of  the  effect  of  different  groups  of  atoms  on  the  character 
of  the  absorption  spectrum  is  attended  with  considerable  diffi- 
culty, but  some  progress  has  been  made  in  this  direction. 
Ultra-red  absorption  spectra  have  a  pronounced  additive  char- 
acter ;  this  is  probably  connected  with  the  generally  accepted 
view  that  absorption  in  this  case  is  connected  with  the  vibrations 
of  the  atoms  themselves. 

Viscosity — The  measurement  of  internal  friction,  or  vis- 
cosity, gives  information  as  to  the  work  done  in  the  relative 
displacement  of  the  particles  of  a  solid,  liquid,  or  gas.  In  the 
case  of  liquids,  for  which  the  property  has  been  most  fully 
investigated,  the  viscosity  is  most  conveniently  studied  by 
observing  the  rate  of  flow  through  capillary  tubes.  We  may 
assume  that  the  layer  of  liquid  in  contact  with  the  wall  of  the 
tube  is  at  rest,  that  the  layer  next  to  it  is  moving  slowly  parallel 
to  the  axis  of  the  tube,  and  that  the  rate  of  movement  gradually 


74          OUTLINES  OF  PHYSICAL  CHEMISTRY 

increases  towards  the  interior,  attaining  its  maximum  at  the 
centre  of  the  tube.  It  is  evident  that  the  rate  of  displacement 
of  the  layers  with  regard  to  each  other  must  be  mainly  deter- 
mined by  the  amount  of  friction  between  them,  and  hence 
measurements  of  the  rate  of  flow  afford  information  as  to  the 
viscosity  of  liquids.  The  converse  of  viscosity  is  termed  fluidify  ; 
a  liquid  of  small  viscosity,  such  as  ether,  is  said  to  have  a  high 
degree  of  fluidity. 

The  magnitude  of  the  viscosity  depends  greatly  on  the 
nature  of  the  liquid.  Thus  the  viscosity  of  warm  ether  is 
very  small,  whereas  that  of  treacle  and  of  pitch  is  so  great  that 
they  approximate  to  the  behaviour  of  solids,  the  internal  friction 
of  which  is  extremely  high.  The  internal  friction  of  gases  is 
very  small  (p.  25). 

The  coefficient  of  viscosity,  r?,  is  usually  defined  as  the  force 
required  to  move  a  layer  of  unit  area  through  a  distance  of 
unit  length  past  an  adjacent  layer  unit  distance  away.  For 
water  at  15°,  TJ  =  0*0134  in  absolute  units;  for  glycerine  at 
the  same  temperature,  77  =  2-34. 

The  coefficient  of  viscosity  of  a  liquid  can  be  calculated 
from  the  rate  of  outflow  from  a  cylindrical  tube  by  means  of 
the  equation 


where  v  is  the  volume  of  liquid  discharged  in  the  time  t,  p  the 
pressure  under  which  the  outflow  takes  place,  r  the  radius  and 
/  the  length  of  the  tube.  In  practice,  however,  the  rate  of 
flow  of  the  liquid  is  compared  with  that  of  a  standard  liquid, 
usually  water,  under  the  same  experimental  conditions,  and  its 
absolute  viscosity,  97,  calculated  by  means  of  the  formula 

I?/I?M  =  t\tn, 

where  vjw  is  the  absolute  viscosity  of  water  at  the  temperature 

of  the  experiment,  and  /  and  /„  are  the  times  required  for  the 

discharge  of  equal  volumes  of  the  liquid  and  water  respectively. 

The  viscosity  of  liquids  diminishes  rapidly  as  the  temperature 


LIQUIDS 


75 


rises,  but  so  far  no  simple  relationship  of  general  applicability 
connecting  change  of  viscosity  and  temperature  has  been  dis- 
covered. 

Measurement  of  Viscosity — The  determination  of  vis- 
cosity by  the  comparative  method  may  be  conveniently  carried 
out  with  the  apparatus  described  by  Ostwald 
and  illustrated  in  Fig.  9.  It  consists  essenti- 
ally of  a  capillary  tube,  db,  connected  at  its 
upper  part  with  a  bulb  k,  and  at  its  lower 
end  with  a  wider  tube,  bent  into  U-shape 
and  provided  with  a  bulb  e.  Marks  are  etched  C 
on  the  capillary  tube  at  c  and  d  above  and 
below  the  bulb  k.  The  apparatus  is  filled  at/ 
with  a  definite  volume  of  the  liquid,  which 
is  then  sucked  into  the  other  limb  till  the 
surface  rises  above  the  mark  c.  The  time 
required  for  the  level  of  the  liquid  to  fall 
from  c  to  d  is  then  noted.  Observations 
have  previously  been  made  with  water  under 
similar  conditions.  As  the  pressures  under 
which  the  discharge  takes  place  are  in  the 
ratio  of  the  density,  d,  of  the  liquid  to  that  of 
water,  the  relative  viscosity,  x  =  77/17,,,  is  given 
by  the  equation 

x  =  dtjdJv. 

On  account  of  the  great  influence  of 
temperature  on  the  viscosity,  the  measure- 
ments must  be  made  at  constant  temperature,  and  for  this 
purpose  the  apparatus  is  so  constructed  that  it  can  conveniently 
be  immersed  in  a  thermostat. 

Results  of  Viscosity  Measurements1 — Reference  has 
already  been  made  to  the  enormous  differences  in  the  viscosity 
of  liquids,  and  also  to  the  fact  that  temperature  has  a  great 
influence  on  the  magnitude  of  the  viscosity.  In  comparing 


FIG.  9. 


1  Smiles,  loc.  cit.  pp.  51-105. 


76 


OUTLINES  OF  PHYSICAL  CHEMISTRY 


different  liquids  with  regard  to  viscosity,  we  are  again  confronted 
with  the  difficulty  of  deciding  at  what  temperatures  the  measure- 
ments should  be  made.  The  choice  of  the  boiling-points  as 
corresponding  temperatures  (p.  57)  did  not  in  this  case  lead 
to  very  satisfactory  results,  and  most  regularities  were  observed 
by  using  the  data  for  points  at  which  the  rate  of  change  of 
viscosity  with  temperature  is  the  same  (Thorpe  and  Rodger). 

A  comparison  of  substances  of  allied  chemical  constitution 
shows  that  viscosity  is  to  some  extent  an  additive  property,  but 
is  greatly  affected  by  constitutive  influences. 

The  absolute  viscosity  of  a  number  of  pure  liquids  at  o°  and 
at  25°  is  given  in  the  accompanying  table  (Walden) : — 


Liquid. 

r;  at  0°. 

r?  at  25°. 

Acetone 

0-00397 

0-00316 

Methyl  alcohol 

0*00846 

0-00580 

Acetic  anhydride 

0-0130 

0-00860 

Water 

0-0178 

0-00891 

Ethyl  alcohol 

0-0179 

O'OIOS 

Benzonitrile 

0-0194 

0-0125 

Nitrobenzene 

0-0307 

0-0182 

In  recent  years  the  viscosity  of  mixtures  of  liquids  has  been 
the  subject  of  a  good  deal  of  investigation.  If  for  simplicity 
we  confine  our  attention  to  mixtures  of  two  components  only, 
three  classes  may  be  distinguished  : — 

(1)  The  viscosity  of  the  mixture  lies  between  those  of  the 
pure  components.     Example,  ethyl  alcohol  and  carbon  disul- 
phide. 

(2)  The  viscosity  of  the  mixture  in  certain  proportions  is 
greater  than  that   of  either  component.       Example,  pyridine 
and  water. 

(3)  The  viscosity  of  the  mixture  in  certain  proportions  is 
less  than  that  of  either  constituent.     Example,  benzene  and 
acetic  acid. 

A  few  numbers  illustrating  the   behaviour  of  the  mixtures 


LIQUIDS 


77 


cited   as   examples   of  classes    (2)  and   (3)  are  given  in  the 
accompanying  table. 


Pyridine  and  Water.i 

Benzene  and  Acetic  Acid.2 

Per  cent. 
Pyridine. 

i)  at  25°. 

Per  cent. 
Benzene. 

r,  at  25°. 

O'OO 

0-00890 

O'OO 

0-01174 

19-28 

0-01336 

34-93 

0-00734 

39-84 

0-01833 

48-29 

0-00666 

597° 

0-02I87 

77-26 

0-00597 

66-65 

O-02225 

89-73 

0-00591 

80-15 

0*01894 

97-25 

0-00594 

lOO'OO 

0-00885 

100-00 

0-00598 

The  results  are  very  similar  to  those  for  the  vapour  pressures 
of  binary  mixtures,  described  later  (p.  87). 

No  general  agreement  has  so  far  been  reached  as  to  the 
explanation  of  these  remarkable  differences  in  the  behaviour  of 
binary  mixtures  (compare  p.  322). 

Measurements  of  the  viscosity  of  salt  solutions  (solutions 
which  conduct  the  electric  current)  have  also  led  to  interesting 
results,  but  they  cannot  be  usefully  considered  at  the  present 
stage. 

Practical  Illustrations,  (a)  Critical  Phenomena — The 
critical  phenomena  can  be  observed  in  an  apparatus,  con- 
structed like  that  of  Cagniard  la  Tour,  but  more  simply  as  fol- 
lows :  A  tube  3-4  mm.  internal  diameter  and  3-4  cm.  long  is 
constructed  out  of  a  piece  of  glass  tubing,  the  walls  of  which 
are  0-7-0-8  mm.  thick,  by  closing  one  end  in  the  blow-pipe  and 
drawing  out  the  other  at  a  distance  3-4  cm.  from  the  closed  end 
into  a  fairly  long  (5-6  cm.)  thick- walled  capillary  tube.  The 
capillary  is  then  bent,  at  a  point  about  i  cm.  from  the  commence- 
ment of  the  wide  part  of  the  tube,  at  right  angles  to  the  latter  and 
then  partly  filled  with  ether  as  follows.  The  tube  is  warmed  and 
the  capillary  end  dipped  into  ether,  which  is  drawn  into  the  tube 

1  Hartley,  Thomas  and  Appleby,  Trans.  Chem.  Soc.,  1908,  94,  538. 
2Dunstan,  ibid.,  1905,  87,  16. 


78         OUTLINES  OF  PHYSICAL  CHEMISTRY 

as  the  latter  cools.  The  ether  in  the  tube  is  then  boiled  gently 
to  expel  all  the  air,  the  end  of  the  capillary  dipping  all  the  time 
in  ether,  and  on  again  allowing  to  cool,  ether  is  drawn  in  so  as 
practically  to  fill  the  tube.  The  excess  of  ether  is  then  boiled 
off  till  the  tube  is  about  three-quarters  full,  the  end  of  the 
capillary  being  in  ether  throughout,  and  then  allowed  to  cool 
till  the  liquid  just  begins  to  rise  up  the  capillary  tube,  showing 
that  the  pressure  inside  is  somewhat  less  than  atmospheric ;  the 
capillary  is  then  rapidly  sealed  off  near  the  bend  on  the  side 
remote  from  the  tube. 

In  order  to  observe  the  capillary  phenomena  in  the  tube 
thus  prepared,  the  latter  is  suspended  by  a  wire  and  heated  by 
means  of  a  Bunsen  burner  held  in  one  hand,  the  face  being 
protected,  in  the  event  of  an  explosion,  by  a  large  plate  of 
glass  held  in  the  other  hand.  In  this  way,  the  complete  dis- 
appearance of  the  liquid  above  a  certain  temperature,  and  its 
reappearance  on  cooling,  may  be  observed  without  the  least 
danger. 

When  practicable,  the  tube  may  be  heated  in  an  iron  or 
copper  vessel  provided  with  mica  windows,  and  the  critical 
temperature  may  be  read  off  on  a  thermometer  placed  side  by 
side  with  the  tube  in  the  air  bath. 

(b)  Determination  of  Molecular  Volume — The  determination 
of  the  molecular  volume  of  a  liquid  reduces  to  a  determination 
of  its  density  at  a  definite  temperature  compared  with  that  of 
water  as  unity,  and  any  of  the  well-known  methods  for  deter- 
mining the  density  of  liquids  may  be  employed  for  this  purpose. 
A  direct  method  for  determining  the  density,  and  hence  the  mole- 
cular volume,  of  a  liquid  at  its  boiling-point  has  been  described 
by  Ramsay.  A  tube  is  drawn  out  to  a  long  neck  and  the  latter 
bent  in  the  form  of  a  hook.  The  vessel  is  then  filled  with 
liquid,  heated  in  the  vapour  of  the  same  liquid  till  equilibrium 
is  reached  and  then  weighed.  If  the  volume  of  the  vessel  and 
its  coefficient  of  expansion  are  known,  the  molecular  volume 
of  the  liquid  can  at  once  be  calculated. 


LIQUIDS  79 

Measurements  of  the  refractive  index  of  liquids  (water 
alcohol,  benzene)  and  of  the  rotation  of  the  plane  of  polarization 
of  light  by  liquids  or  solutions  (cane  sugar  in  water)  should  be 
made  by  the  student ;  the  methods  are  fully  described  in  text- 
books of  physics.  The  experiments  on  rotation  of  the  plane 
of  polarization  may  conveniently  be  made  in  connection  with 
the  hydrolysis  of  cane  sugar  in  the  presence  of  acids  (p.  230). 


CHAPTER    IV 
SOLUTIONS 

General — Up  to  the  present,  we  have  dealt  only  with  the 
properties  of  pure  substances  which  may  exist  in  the  gaseous, 
liquid  or  solid  state,  or  simultaneously  in  two  or  all  of  these 
states.  We  now  proceed  to  deal  with  the  properties  of  mixtures 
of  two  or  more  pure  substances.  When  these  mixtures  are 
homogeneous,  they  are  termed  solutions.1  There  are  various 
classes  of  solutions,  depending  on  the  state  of  the  components. 
The  more  important  are  : — 

(i)  Solutions  of  gases  in  gases  ; 

(ii)  Solutions  of  (a)  gases,  (b)  liquids,  (c)  solids  in  liquids  ; 

(iii)  Solutions  of  solids  in  solids,  so-called  solid  solutions ; 
and  each  of  these  classes  will  be  briefly  considered. 

A  distinction  is  often  drawn  between  solvent  and  dissolved 
substance,  but,  as  will  appear  particularly  from  the  sections 
dealing  with  the  mutual  solubility  of  liquids,  there  is  no  sharp 
distinction  between  the  two  terms.  The  component  which  is 
present  in  greater  proportion  is  usually  termed  the  solvent. 
The  dissolved  substance  is  sometimes  called  the  solute. 

When  one  of  the  compounds  is  present  in  very  small  pro- 
portion, the  system  is  termed  a  dilute  solution,  and  as  the  laws 

xThe  term  solution  is  also  applied  to  mixtures  which  appear  homo- 
geneous to  the  naked  eye  but  heterogeneous  when  examined  with  a  micro- 
scope or  ultramicroscope,  e.g.,  colloidal  solution  of  arsenic  sulphide. 

The  usual  definition  of  a  solution  is  "a  homogeneous  mixture  which 
cannot  be  separated  into  its  components  by  mechanical  means,"  but  the 
last  part  of  this  definition  is  open  to  objection. 

80 


SOLUTIONS 


81 


representing  the  behaviour  of  dilute  solutions  are  comparatively 
simple,  they  will  be  dealt  with  separately  in  the  next  chapter. 

Solution  of  Gases  in  Gases — This  class  of  solution  differs 
from  the  others  in  that  the  components  may  be  present  in  any 
proportion,  since  gases  are  completely  miscible.  If  no  chemical 
change  takes  place  on  mixing  two  gases,  they  behave  quite  in- 
dependently and  the  properties  of  the  mixture  are  therefore  the 
sum  of  the  properties  of  the  constituents.  In  particular,  the 
total  pressure  of  a  mixture  of  gases  is  the  sum  of  the  pressures 
which  would  be  exerted  by  each  of  the  components  if  it  alone 
occupied  the  total  volume — a  law 
which  was  discovered  by  Dalton,  and 
is  known  as  Dalton  s  law  of  partial 
pressures.  Dalton's  law  is  of  the  same 
order  of  validity  as  Avogadro's  hy- 
pothesis ;  it  is  nearly  true  under 
ordinary  conditions,  and  would  in 
all  probability  become  strictly  true 
at  great  dilution. 

Dalton's  law  can  of  course  be 
tested  by  comparing  the  sum  of  the 
pressures  exerted  separately  by  two 
gases  with  that  after  admixture,  but 
it  is  of  interest  to  inquire  into  the 
possibility  of  measuring  the  partial 
pressure  of  one  of  the  components 
in  the  mixture  itself.  It  was  pointed 

out  by  van't  Hoff  that  this  is  always  possible  if  a  membrane 
can  be  obtained  which  allows  only  one  of  the  gases  to  pass 
through.  This  suggestion  was  experimentally  realised  by  Ram- 
say x  in  the  case  of  a  mixture  of  nitrogen  and  hydrogen  as 
follows:  P  (Fig.  10.)  is  a  palladium  vessel  containing  nitrogen, 
the  pressure  of  which  can  be  determined  from  the  difference 
of  level  between  A  and  B  in  the  manometer,  which  contains 
mercury.  P  is  enclosed  in  another  vessel,  which  can  be  filled 


FIG.  10. 


1  Phil.  Mag.,  1894,  [v.],  38,  206. 


82          OUTLINES  OF  PHYSICAL  CHEMISTRY 

with  hydrogen  at  any  desired  pressure.  The  vessel  P  is  heated 
and  a  stream  of  hydrogen  at  known  pressure  passed  through  the 
outer  vessel.  As  palladium  at  high  temperatures  is  permeable 
for  hydrogen,  but  not  for  nitrogen,  the  former  gas  enters  P  till 
its  pressure  outside  and  inside  are  equal.  The  total  pressure  in 
P,  as  measured  on  the  manometer,  is  greater  than  the  pressure 
in  the  outer  vessel,  and  it  is  an  experimental  fact  that  the 
excess  pressure  inside  is  approximately  equal  to  the  partial 
pressure  of  the  nitrogen. 

If,  on  the  other  hand,  we  start  with  a  mixture  of  hydrogen  and 
nitrogen,  and  wish  to  find  the  partial  pressure  of  the  latter,  all 
that  is  necessary  is  to  put  the  mixture  inside  a  palladium  bulb, 
keep  the  latter  at  a  constant  high  temperature  and  pass  a  current 
of  hydrogen  at  known  pressure  through  the  outer  vessel  till  equi- 
librium is  attained,  as  shown  on  the  manometer.  The  difference 
between  the  external  and  internal  pressure  is  then  the  partial 
pressure  of  the  nitrogen.  This  very  instructive  experiment  will 
be  referred  to  later  in  connection  with  the  modern  theory  of 
solutions  (p.  101). 

Solubility  of  Gases  in  Liquids — In  contrast  to  the  com- 
plete miscibility  of  gases,  liquids  are  only  capable  of  dissolving 
gases  to  a  limited  extent.  When  a  liquid  will  not  take  up  any 
more  of  a  gas  at  constant  temperature  it  is  said  to  be  saturated 
with  the  gas,  and  the  resulting  solution  is  termed  a  saturated 
solution.  The  amount  of  a  gas  taken  up  by  a  definite  volume 
of  liquid  depends  on  (a)  the  pressure  of  the  gas,  (b)  the  tem- 
perature, (c)  the  nature  of  the  gas,  (d)  the  nature  of  the  liquid. 

The  greater  the  pressure  of  a  gas,  the  greater  is  the  quantity 
of  it  taken  up  by  the  solvent.  For  gases  which  are  not  very 
soluble,  and  do  not  enter  into  chemical  combination  with  the 
solvent,  the  relation  between  pressure  and  solubility  is  expressed 
by  Henry's  law  as  follows  :  The  quantity  of  gas  taken  up  by  a 
given  volume  of  solvent  is  proportional  to  the  pressure  of  the  gas. 
Another  way  of  stating  Henry's  law  is  that  the  volume  of  a  gas 
taken  up  by  a  given  volume  of  solvent  is  independent  of  the 


SOLUTIONS  83 

pressure.  This  is  clearly  equivalent  to  the  first  statement,  be- 
cause when  the  pressure  is  doubled  the  quantity  of  gas  absorbed 
is  doubled,  but  since  its  volume,  by  Boyle's  law,  is  halved,  the 
original  and  final  volumes  dissolved  are  equal. 

The  question  may  be  regarded  from  a  slightly  different  point 
of  view,  which  is  instructive  in  connection  with  later  work. 
When  a  definite  volume  of  liquid  is  saturated  with  a  gas  at  a 
certain  pressure,  there  is  an  equilibrium  between  the  dissolved 
gas  and  that  over  the  liquid,  and  Henry's  law  may  be  expressed 
in  the  alternative  form  :  The  concentration  of  the  dissolved  gas  is 
proportional  to  that  in  the  free  space  above  the  liquid.  We  may 
consider  that  the  gas  distributes  itself  between  the  solvent  and 
the  free  space  in  a  ratio  which  is  independent  of  the  pressure. 
The  solubility  of  gases  in  liquids  diminishes  fairly  rapidly  with 
rise  of  temperature. 

For  purposes  of  comparison,  the  solvent  power  of  a  liquid  for 
a  gas  is  best  expressed  in  terms  of  the  "  coefficient  of  solubility," 
which  is  the  volume  of  the  gas  taken  up  by  unit  volume  of  the 
liquid  at  a  definite  temperature.1  The  so-called  "absorption 
coefficient  "  of  Bunsen,  in  which  solubility  measurements  are 
still  often  expressed,  is  the  volume  of  a  gas,  reduced  to  o°  and 
76  cm.  pressure,  which  is  taken  up  by  unit  volume  of  a  liquid 
at  a  definite  temperature  under  a  gas  pressure  equal  to  76  cm. 
of  mercury. 

With  regard  to  the  influence  of  the  nature  of  the  gas  on  the 
solubility,  it  may  be  said  in  general  that  gases  which  have 
distinct  basic  or  acidic  properties,  for  example,  ammonia  and 
hydrogen  chloride,  are  very  soluble,  whilst  neutral  gases,  such  as 
hydrogen,  oxygen  and  nitrogen,  are  comparatively  insoluble. 
Further,  gases  which  are  easily  liquefied,  for  example,  sulphur 
dioxide  and  hydrogen  sulphide,  are  fairly  soluble. 

As  regards  the  relation  between  solvent  power  and  the  nature 
of  the  liquid,  very  little  is  known.  In  general,  the  order  of 
the  solubility  of  gases  in  different  liquids  is  the  same,  and 
the  solvent  power  of  a  liquid  therefore  appears  to  be  to  some 
extent  a  specific  property. 

1  Alternatively  :  the  ratio  of  the  concentration  in  liquid  and  in  gas  space. 


84 


OUTLINES  OF  PHYSICAL  CHEMISTRY 


The  above  remarks  are  illustrated  by  the  following  table,  in 
which  the  coefficients  of  solubility  of  some  typical  gases  in  water 
and  in  alcohol  are  given  : — 


Gas. 

Water. 

Alcohol. 

Ammonia 

1050 

Hydrogen  sulphide 
Carbon  dioxide 

80 
r8 

18 
4'3 

Oxygen   . 

0*04 

0-28 

Hydrogen 

O'O2 

0-07 

It  may  be  mentioned  that  the  solubility  of  gases  in  water  is 
greatly  diminished  by  the  addition  of  salts,  and  to  a  much 
smaller  extent  by  non-electrolytes.  The  interpretation  of  these 
results  has  given  rise  to  considerable  difference  of  opinion.1 

Solubility  of  Liquids  in  Liquids — As  regards  the  mutual 
solubility  of  liquids,  three  cases  may  be  distinguished  :  (i)  The 
liquids  mix  in  all  proportions,  e.g.,  alcohol  and  water  ;  (2)  the 
liquids  are  practically  immiscible,  e.g.,  benzene  and  water ;  (3) 
the  liquids  are  partially  miscible,  e.g.,  ether  and  water. 

(i)  and  (2)  Complete  miscibility  and  non-miscibility — Very 
little  is  known  as  to  the  factors  which  determine  the  miscibility 
or  non-miscibility  of  liquids.  The  separation  of  the  compon- 
ents by  fractional  distillation  is  discussed  in  succeeding  sections. 

(3)  Partial  miscibility — If  ether,  in  gradually  increasing 
amounts,  is  added  to  water  in  a  separating-funnel,  and  the  mix- 
ture well  shaken  after  each  addition,  it  will  be  noticed  that  at 
first  a  homogeneous  solution  is  formed,  but  when  sufficient 
ether  has  been  added,  a  separation  into  two  layers  takes  place 
on  standing.  The  upper  layer  is  a  saturated  solution  of  water 
in  ether,  the  lower  layer  a  saturated  solution  of  ether  in  water. 
As  long  as  the  relative  quantities  of  ether  and  water  are  such 
that  a  separation  into  two  layers  takes  place  on  standing,  the 

1  Compare  Philip,  Trans.  Chcm.  Soc.t  1907,  91,  711;  Usher,  ibid., 
1910,  97,  66. 


SOLUTIONS  85 

composition  of  these  layers  is  independent  of  the  relative  amounts 
of  the  components  present,  since  the  composition  is  determined 
by  the  solubility  of  ether  in  water  and  of  water  in  ether  at  the 
temperature  of  experiment. 

In  the  majority  of  cases,  the  solubility  of  two  partially 
miscible  liquids  increases  with  the  temperature,  and  it  may 
therefore  be  anticipated  that  liquids  which  in  certain  propor- 
tions form  two  layers  at  the  ordinary  temperature  may  be  com- 
pletely miscible  at  higher  temperatures.  Several  such  cases 
are  known,  ior  example,  phenol  and  water,  and  aniline  and 
water,  which  have  been  investigated  by  Alexieeff.  He  took 
the  components  in  varying  proportions,  and  gradually  raised 
the  temperature  till  the  mixture  became  homogeneous.  The 
results  with  phenol  and  water  are  represented  graphically  in 
Fig.  1 1, the  composition  of  the  mixture  being  measured  on  the 
horizontal  axis  and  temperatures  along  the  vertical  axis.  The 
point  D  represents  o  per  cent,  phenol  (100  per  cent,  water),  E 
represents  100  per  cent,  phenol.  At  all  points  outside  the 
curve  ABC  there  is  complete  miscibility,  at  points  inside  the 
curve  two  layers  exist.  The  maximum  represents  the  tem- 
perature, 68 '4°,  above  which  phenol  and  water  are  miscible 
in  all  proportions.  If,  therefore,  we  start  with  a  homogeneous 
solution  of  phenol  in  water  of  the  composition  represented 
by  the  point  of,  and  gradually  add  phenol  at  constant  tem- 
perature, the  composition  of  the  solution  will  alter  along  the 
dotted  line  xx'  until  the  curve  AB  is  reached  at  z.  This 
point  represents  a  saturated  solution  of  phenol  in  water,  and 
on  further  addition  of  phenol  a  separation  into  two  layers 
takes  place,  the  compositions  of  which  are  represented  by  the 
points  z  and  z1  respectively.  As  more  phenol  is  added,  the 
composition  of  the  layers  remains  unaltered,  but  the  relative 
amount  of  the  second  layer  increases  until  at  the  point  z'  only 
this  layer  is  present,  and  its  composition  then  alters  along  zx' . 
If,  however,  phenol  is  added  to  the  same  solution  at  the  tem- 
perature corresponding  with  the  point  y  the  composition  alters 


86 


OUTLINES  OF  PHYSICAL  CHEMISTRY 


along  yy  but  no  separation  into  two  layers  takes  place.  It  is 
evident  that  there  is  a  striking  analogy  between  the  miscibility 
of  two  liquids  and  the  critical  phenomena  represented  in  Fig. 
5.  In  both  cases  there  is  only  one  phase  outside  the  curves 


210 


A  C 

100  o/0 
Phenol 
Miscibility  of  Phenol  and  Water. 

FIG.  ii. 


0°/0 

Phenol 


GO 


0% 

Nicotine 


10OA> 

Nicotine 


Miscibility  of  Nicotine  and  Water. 

FIG.  12. 


AOE  and  ABC  respectively,  and  two  phases  at  points  inside 
the  curves.  Further,  above  a  certain  temperature  only  one 
phase  can  exist  in  each  case,  and  the  temperature  of  com- 
plete miscibility  for  binary  mixtures  may  therefore  be  termed 
the  critical  solution  temperature.  Moreover,  just  as  we  can 


SOLUTIONS  87 

pass  without  discontinuity  from  a  gas  to  a  liquid  (p.  53),  we  can 
pass  from  a  solution  containing  excess  of  water  to  one  contain- 
ing excess  of  phenol  without  discontinuity.  Starting  with  a 
mixture  represented  by  the  point  x,  the  temperature  is  raised 
above  the  critical  solution  temperature  along  xy,  phenol  is  then 
added  till  the  point  y  is  reached  and  the  homogeneous  mixture 
then  cooled  along  y'x. 

In  some  cases,  however,  the  solubility  of  one  liquid  in  another 
diminishes  with  rise  of  temperature,  thus  if  a  saturated  solution 
of  ether  in  water,  prepared  at  the  ordinary  temperature,  is  gently 
warmed,  it  becomes  turbid,  indicating  partial  separation  of  the 
ether.  An  interesting  example  of  this  behaviour  is  seen  in 
nicotine  and  water,  which  are  miscible  in  all  proportions  at  the 
ordinary  temperature,  but  separate  into  two  layers  when  the 
temperature  reaches  60°.  If  a  temperature  can  be  reached 
beyond  which  the  mutual  solubility  again  begins  to  increase 
with  rise  of  temperature,  the  components  may  again  become 
miscible  in  all  proportions.  This  has  been  experimentally 
realised  so  far  only  for  nicotine  and  water,  which  again  be- 
come completely  miscible  when  the  temperature  exceeds  210°. 
The  remarkable  solubility  relations  of  these  two  liquids  are 
therefore  represented  by  a  closed  curve  (Fig.  12),  which  will 
be  readily  understood  by  comparison  with  Fig.  n. 

Distillation  of  Homogeneous  Mixtures — A  very  impor- 
tant matter  with  reference  to  binary  homogeneous  mixtures  is 
the  possibility  of  separating  them  more  or  less  completely  into 
their  components  by  distillation.  Much  light  is  thrown  on  this 
question  by  the  investigation  of  the  vapour-pressure  of  the  mix- 
ture as  a  function  of  its  composition  at  constant  temperature. 
Experimental  investigation  shows  that  the  curve  representing  the 
relation  between  vapour  pressure  and  composition  at  constant 
temperature  usually  belongs  to  one  of  the  three  main  types  a, 
b  and  c  represented  in  Fig.  13,  in  which  the  abscissae  represent 
the  composition  of  the  mixture  and  the  ordinates  the  corres- 
ponding vapour  pressures. 


88 


OUTLINES  OF  PHYSICAL  CHEMISTRY 


(a)  The  vapour-pressure  curve  of  the  mixture  may  have  a 
minimum,  as  represented  by  the  point  U  in  the  curve  RUS ; 
example,  hydrochloric  acid  and  water.  (In  the  diagram  the 
ordinate  PR  represents  the  vapour-pressure  of  B,  and  QS  that  of 
the  other  pure  substance  A.) 

(ft)  The  vapour-pressure  curve  may  show  a  maximum,  repre- 
sented by  the  point  T  on  the  curve  RTS ;  example,  propyl 
alcohol  and  water. 


P(o°/0  A) 


Composition 

FIG.  13. 


Q  (100  °/0  A) 


(c)  The  vapour-pressure  of  the  binary  mixture  may  lie 
between  those  of  the  pure  components  A  and  B,  as  repre- 
sented by  the  curve  RWS ;  example,  methyl  alcohol  and 
water. 

In  considering  these  three  typical  cases  with  regard  to  their 
bearing  on  the  separation  of  two  liquids  by  fractional  distilla- 
tion, the  important  question  is  the  relation  between  the  com- 
position of  the  boiling  liquid  and  that  of  the  escaping  vapour. 
For  a  pure  liquid,  the  composition  of  the  escaping  vapour  is 
necessarily  the  same  as  that  of  the  liquid,  but  this  is  not  in 
general  the  case  for  a  mixture  of  liquids,  and  therefore  the 


SOLUTIONS  89 

composition  of  the  mixture  may  alter  continuously  during  dis- 
tillation. 

Case  (a).  Since  a  liquid  boils  when  its  vapour  pressure  is 
equal  to  the  external  pressure,  it  is  clear  that  if  a  mixture  the 
vapour-pressure  curve  of  which  has  a  minimum  (as  in  the  curve 
RUS)  be  boiled,  the  composition  of  the  liquid  will  alter  in 
such  a  way  that  it  tends  to  approximate  to  that  represented  by 
the  point  U,  since  all  other  mixtures  have  a  higher  vapour 
pressure,  and  will  consequently  pass  off  first.  When  finally 
only  the  mixture  U  remains,  it  will  distil  at  constant  tempera- 
ture like  a  homogeneous  liquid,  since  the  composition  of  the 
vapour  is  then  the  same  as  that  of  the  liquid.  The  best- 
known  example  of  such  a  constant-boiling  liquid  is  a  mixture  of 
hydrochloric  acid  and  water,  which  boils  at  no0.  If  a  mixture 
containing  the  components  in  any  other  proportion  be  heated, 
either  hydrochloric  acid  or  water  will  pass  off,  and  the  com- 
position of  the  liquid  will  move  along  the  curve  to  the  point 
of  minimum  vapour  pressure,  beyond  which  it  distils  as  a  whole, 
without  further  change  of  composition. 

Case  (b).  When,  on  the  other  hand,  there  is  a  maximum  in 
the  vapour-pressure  curve,  the  mixture  which  has  the  highest 
vapour  tension  will  pass  over  first,  and  the  composition  of  the 
residue  in  the  retort  will  tend  towards  the  component  which 
was  present  in  excess  in  the  initial  mixture.  In  the  case  of 
propyl  alcohol  and  water,  for  example,  the  mixture  which  has 
the  highest  vapour  tension  contains  from  70  to  80  per  cent. 
alcohol  (the  maximum  being  very  flat) ;  a  mixture  of  this  com- 
position would  boil  at  constant  temperature,  whilst  for  one  con- 
taining more  water,  some  of  the  latter  would  finally  remain  in 
the  retort. 

Case  (c).  In  this  case  the  composition  of  the  vapour,  and 
therefore  the  composition  of  the  liquid  remaining,  alter  continu- 
ously on  distillation.  The  vapour,  and  therefore  the  distillate, 
will  contain  the  more  volatile  liquid,  A,  in  greater  proportion,  and 
the  residue  excess  of  the  less  volatile  liquid,  a  partial  separation 


90         OUTLINES  OF  PHYSICAL  CHEMISTRY 

being  thus  effected.  If  the  distillate  rich  in  A  is  again  distilled 
a  mixture  still  richer  in  A  is  at  first  given  off,  and  the  process 
may  be  repeated  again  and  again.  The  more  or  less  complete 
separation  of  liquids  by  this  method  is  termed  fractional  dis- 
tillation. 

It  was  long  thought  that  constant-boiling  mixtures  were 
definite  chemical  compounds  of  the  two  components — for 
example,  HC1,  8H2O  in  the  case  of  hydrochloric  acid  and 
water,  but  this  view  was  shown  by  Roscoe  to  be  untenable. 
He  found  that  the  composition  of  the  mixtures  does  not 
correspond  with  simple  molecular  proportions  of  the  com- 
ponents, and,  further,  that  the  composition  alters  con- 
tinuously with  alteration  of  the  pressure  under  which  the 
distillation  is  conducted,  which  is  not  likely  to  be  the  case  if 
definite  chemical  compounds  are  present. 

Distillation  of  Non-Miscible  or  Partially  Miscible 
Liquids.  Steam  Distillation — If  two  immiscible  liquids  are 

distilled  from  the  same 
vessel,  since  one  does 
not  affect  the  vapour 
pressure  of  the  other, 


they  will  pass  over  in 
the  ratio  of  the  vapour 
pressures  till  one  of  them 
is  used  up.  The  tem- 
perature .  at  which  the 
mixture  boils  is  that  at 
which  the  sum  of  the 
vapour  pressures  is  equal 
P(o°/0B)  Composition  Q  100  °/0  B)  to  the  superincumbent 

FlG4  I4  pressure.     The  curve  re- 

presenting   the    relation 

between  vapour  pressure  and  composition  of  the  mixture  is 
therefore  a  straight  line  (UU',  Fig.  14)  parallel  to  the  axis  of 
composition,  PU  representing  the  sum  of  the  vapour  pressures 


SOLUTIONS  91 

RP  and  QT,  of  the  two  components  at  the  temperature  in 
question. 

These  considerations  are  very  important  in  connection  with 
steam-distillation.  This  process  is  usually  employed  for  the 
separation  of  substances  with  a  high  boiling-point,  such  as 
aniline,  and  will  be  familiar  to  the  student.  The  relative 
volumes  of  steam  and  the  vapour  of  the  liquid  which  pass  over 
are  in  the  ratio  of  the  vapour  pressures,  p^  and  /2,  at  the  tem- 
perature of  the  experiment,  and  the  relative  weights  which  pass 
over  are  therefore  in  the  ratio  p^  :  /2</2,  in  which  d^  and  d^  are 
the  densities  of  steam  and  of  the  other  vapour  respectively. 
Assuming  that  the  system  aniline-water  boils  at  98°,  at  which 
temperature  the  vapour  pressure  of  water  is  707  mm.  (/j),  the 
partial  pressure  of  the  aniline  (/2)  wn"l  De  760-  707  =  53  mm., 
and  the  weights  of  aniline  and  water  which  pass  over  are  in 
the  ratio  53  x  93  :  707x18  or  4929  :  12,726.  This  shows 
that  under  ideal  conditions  the  ratio  of  water  to  aniline  in  the 
distillate  is  approximately  2*5  :  r,  the  comparatively  small  vapour 
pressure  of  aniline  being  partially  compensated  for  by  its  rela- 
tively high  molecular  weight. 

Finally,  we  consider  the  distillation  from  the  same  vessel 
of  partially  miscible  liquids.  The  relation  between  vapour 
pressure  and  composition  of  the  mixture  in  this  case  is  repre- 
sented by  the  curve  RSST  (Fig.  14),  RP  representing  the  vapour 
pressure  of  the  pure  component  A,  and  QT  that  of  the  other 
component  B.  In  general,  the  vapour  pressure  of  one  liquid 
is  lowered  by  the  addition  of  another.  It  follows  that  the 
vapour  pressure  of  partially  miscible  liquids,  as  long  as  two 
layers  are  present,  will  be  represented  by  a  straight  line  parallel 
to  the  axis  of  composition,  but  lower  than  the  line  UU'  repre- 
senting the  sum  of  the  separate  vapour  pressures.  The  pressures 
when  only  one  phase  is  present  are  represented  by  RS  and  ST 
respectively. 

Solution  of  Solids  in  Liquids — In  this  case  the  solubility 
is  always  limited,  and  depends  on  the  nature  of  the  solvent 


92         OUTLINES  OF  PHYSICAL  CHEMISTRY 

and  solute  and  on  the  temperature.  As  in  the  other  cases 
of  solubility  we  are  really  dealing  with  an  equilibrium,  in  this 
case  between  the  dissolved  salt  and  the  solid. 

Two  principal  methods  are  employed  for  determining  the 
solubility  of  solids  in  liquids,  (i)  Excess  of  the  finely-divided 
solid  is  shaken  continuously  with  a  definite  quantity  of  the 
solvent  at  a  definite  temperature  till  equilibrium  is  attained; 
(2)  the  solvent  is  heated  with  excess  of  the  solute  to  a  tem- 
perature higher  than  that  at  which  the  solubility  is  to  be 
determined,  and  then  cooled  to  the  desired  temperature  in 
contact  with  the  solid.  The  second  method  is  to  be  recom- 
mended when  sufficient  time  is  allowed  for  the  attainment  of 
equilibrium  at  the  temperature  of  experiment,  but  with  suitable 
precautions  the  methods  give  identical  results. 

It  is  of  interest  to  note  that  the  solubility  depends  somewhat 
upon  the  state  of  division  of  the  solids  ;  the  more  finely  divided 
the  solid  the  greater  is  the  solubility.  For  fairly  soluble  salts 
the  difference  is  negligible,  but  for  slightly  soluble  salts  it  may 
be  relatively  very  considerable.  Thus  Ostwald  has  shown  that 
the  solubility  in  water  of  yellow  oxide  of  mercury  is  about  14 
per  cent,  greater  than  that  of  the  coarser-grained  red  modification. 

The  results  of  solubility  measurements  may  be  expressed  in 
various  ways,  for  example,  as  the  number  of  grams  of  solute 
in  100  grams  of  the  solvent,  in  100  grams  of  the  solution,  or 
in  TOO  c.c.  of  the  solution. 

When  a  solution  saturated  at  a  high  temperature  is  allowed 
to  cool  in  the  complete  absence  of  the  solid  solute,  the  excess 
of  dissolved  substance  may  not  separate  (cf.  p.  55),  and  the 
solution  is  then  said  to  be  supersaturated. 

Effect  of  Change  of  Temperature  on  the  Solubility  of 
Solids  in  Liquids — The  variation  of  the  solubility  in  water  of 
certain  salts  with  change  of  temperature  is  shown  in  Fig.  15, 
the  solubilities  being  represented  as  ordinates  and  the  tempera- 
tures as  abscissae.  The  curves  are  not  drawn  to  scale,  but 
represent  diagram  matically  the  effect  of  change  of  temperature. 


SOLUTIONS 


93 


The  solubility  of  most  solids  in  water  increases  fairly  rapidly 
with  the  temperature,  e.g.,  potassium  nitrate;  but  sodium 
chloride  is  only  slightly  more  soluble  in  hot  than  in  cold  water. 
Calcium  hydroxide  and  certain  other  calcium  salts  are  less 
soluble  in  hot  than  in  cold  water;  a  solution  of  calcium 
hydroxide  (lime  water)  saturated  at  the  ordinary  temperature, 


Temperature— > 
FIG.  15. 

becomes  turbid  on  warming.  In  the  case  of  calcium  sulphate, 
the  solubility  increases  at  first  with  rise  of  temperature  and  then 
diminishes,  so  that  there  is  a  maximum  in  the  solubility  curve, 
as  shown  in  the  figure. 

Solubility  curves  are  usually  continuous,  but  that  representing 
the  solubility  of  sodium  sulphate  shows  a  distinct  change  of 
direction  at  33°.  This  is  owing  to  the  fact  that  we  are  dealing 


94         OUTLINES  OF  PHYSICAL  CHEMISTRY 

with  the  solubility  curves  of  two  distinct  substances.  Below 
33°,  the  dissolved  salt  is  in  equilibrium  with  the  solid  deca- 
hydrate  Na2SO4,  ioH2O,  but  the  latter  splits  up  into  the 
anhydrous  salt  and  water  at  33°,  so  that  the  solubility  curve 
at  higher  temperatures  is  that  of  the  anhydrous  salt.  That 
this  explanation  of  the  phenomenon  is  correct  is  shown  by  the 
fact  that  the  solubility  of  the  anhydrous  salt  can  be  determined 
for  a  few  degrees  below  33°  in  the  complete  absence  of  crystals 
of  the  decahydrate ;  the  part  of  the  curve  thus  obtained,  repre- 
sented by  the  dotted  line,  is  continuous  with  the  right-hand 
curve. 

It  is  important  to  remember  that  the  change  to  which  the 
break  in  the  solubility  curve  of  sodium  sulphate  is  due  takes 
place  in  the  solid  phase  and  not  in  the  solution.  No  well- 
defined  case  is  known  of  a  sharp  break  in  a  curve  representing 
the  variation  of  a  physical  property  in  a  homogeneous  system 
with  temperature  or  composition. 

Relation  between  Solubility  and  Chemical  Constitution 
— Very  little  is  known  as  to  causes  influencing  the  mutual 
solubility  of  substances  and  its  variation  with  temperature.  In 
general,  it  may  be  said  that  substances  of  similar  chemical  com- 
position are  mutually  soluble,  thus  the  paraffins  are  miscible 
with  each  other  in  all  proportions,  and  organic  compounds 
containing  the  hydroxyl  group  are  all  fairly  soluble  in  water. 
In  these  cases  it  does  not  seem  probable  that  the  solubility 
is  connected  with  anything  in  the  nature  of  ordinary  chemical 
combination.  Phenomena  of  an  apparently  different  nature  are 
met  with  in  the  solubility  of  gases  in  liquids,  already  referred 
to  (p.  83),  where  it  was  pointed  out  that  the  solvent  power  is 
in  general  a  specific  property  of  the  solute,  and  to  some 
extent  independent  of  the  nature  of  the  gas.  The  solubility 
of  indifferent  gases  appears  in  the  first  instance  to  depend  upon 
the  relative  ease  with  which  they  can  be  liquefied. 

Solid  Solutions  * — In  general,  when  the  temperature  of  a 
dilute  solution  is  lowered  until  partial  solidification  takes  place, 

1  Compare  Bruni,  Feste  Losnngen  und  Isomorphismus,  Leipzig,  1908. 


SOLUTIONS  95 

the  solvent  separates  in  the  solid  form,  practically  uncontami- 
nated  with  the  solute.  When,  however,  a  solution  of  iodine  in 
benzene  is  partially  frozen,  crystals  containing  both  substances 
separate,  and  when  solutions  of  varying  concentration  are  used, 
there  is  a  constant  ratio  between  the  iodine  remaining  in  solution 
and  that  in  the  solidified  benzene.  This  is  illustrated  in  the 
accompanying  table  ;  in  the  top  line  is  given  the  concentration 
Cj  of  the  iodine  in  the  liquid  benzene,  in  the  second  line  the 
iodine  concentration  C2  in  the  solid  benzene,  and  in  the  third 
line  the  ratio  of  the  concentrations  in  solid  and  liquid,  which  is 
approximately  constant  :  — 

'  Cj  3-39         2-587       0-945       per  cent. 

C2  1-279       0-925       0-317       percent. 

0-377       0-358       0-336 


This  phenomenon  exactly  corresponds  with  Henry's  law  regard- 
ing the  solubility  of  gases  in  liquids  (p.  82),  and  as  the  crystals 
containing  the  two  substances  are  quite  homogeneous,  they  may 
be  regarded  as  a  solid  solution  of  iodine  in  benzene.  Similar 
phenomena  have  been  observed  for  many  other  pairs  of  sub- 
stances, more  particularly  for  certain  metals  (p.  192). 

Besides  crystalline  solid  solutions,  of  which  an  example  has 
just  been  given,  non-crystalline  or  amorphous  solid  solutions 
are  known.  The  hydrogen  absorbed  by  palladium  appears  to 
be  in  solid  solution  in  the  metal,  but  the  phenomenon  is  com- 
plicated, and  is  not  yet  thoroughly  understood.  Van't  Hoff 
suggests  that  two  solid  solutions  are  present,  hydrogen  dissolved 
in  palladium  and  palladium  dissolved  in  solid  hydrogen,  corre- 
sponding with  the  two  liquid  layers  formed  by  phenol  and 
water. 

There  is  evidence  that  in  some  cases  the  dissolved  substances 
can  diffuse  slowly  through  the  solid  solvent,  which  indicates  that 
the  solute  exerts  osmotic  pressure  (p.  97). 

Practical  Illustrations,  (a)  Partial  Miscibility  —  The 
fact  that  certain  liquids,  such  as  phenol  and  water,  are  only 


96          OUTLINES  OF  PHYSICAL  CHEMISTRY 

partially  miscible  at  ordinary  temperatures,  but  completely 
miscible  above  69°,  may  be  illustrated  as  follows:  5-6  grams 
of  crystals  of  phenol  are  placed  in  a  small  separating  funnel, 
and  on  adding  a  little  water  and  shaking  it  will  be  found  that 
a  clear  solution  is  formed,  mainly  due  to  the  effect  of  water 
in  lowering  the  freezing-point  of  phenol.  On  further  addition 
of  water  two  layers  will  be  formed,  which  only  disappear  when 
a  large  excess  of  water  has  been  added.  If,  on  the  other 
hand,  phenol  is  warmed  to  75°  in  a  test  tube,  and  water  at 
the  same  temperature  is  gradually  added,  no  separation  into 
two  layers  will  occur,  corresponding  with  the  fact  that  the 
critical  solution  temperature  has  been  exceeded. 

(b)  Solubility  and  Temperature — The  solubility  in  water  of  a 
salt  such  as  sodium  chloride  may  conveniently  be  determined 
as  follows.     A  large  test  tube  is  partially  filled  with  distilled 
water  and  excess  of  powdered  sodium  chloride,  and  partially 
immersed  in  a  bath  kept  at  constant  temperature.     The  tube  is 
closed  by  means  of  a  rubber  cork  through  which  passes  a  glass 
stirrer,  driven  by  means  of  a  motor.     At  intervals  samples  of 
the  solution  are  removed  by  means  of  a  pipette,  a  weighed 
portion  of  the  solution  evaporated  to  dryness,  and  the  residue 
weighed.     When  the  concentration  of  the  solution  no  longer 
alters,  it  is  saturated.     Observations  should  be  made  at  differ- 
ent temperatures  at  intervals  of  10°  and  the  results  plotted  on 
squared  paper,  the  temperatures  being  plotted  as  abscissae,  and 
the  solubility  expressed  as  grams  of  the  salt  in  100  grams  of 
solvent,  as  ordinates  (Fig.  15). 

(c)  Supersaturated  Solutions — A  supersaturated  solution  of 
sodium  sulphate  may  be  prepared  by  heating  the  salt  with  half 
its  weight  of  water  in  a  flask  till  a  perfectly  clear  solution  is 
obtained;  the  flask  is  then  plugged  with  cotton  wool  and  set 
aside  to  cool.     If  a  small  crystal  of  the  sulphate  is  added  to 
the  cold  solution,  crystallization  at  once  starts,  but  crystals  not 
isomorphous    with    sodium    sulphate    (e.g.,    sodium    chloride 
crystals)  are  not  efficient  in  starting  crystallization. 


CHAPTER   V 
DILUTE   SOLUTIONS 

General — So  far,  we  have  dealt  in  a  general  way  with  the 
properties  of  solutions,  mainly  on  the  lines  of  the  older  methods 
of  investigation,  as  they  were  practised  up  to  about  twenty 
years  ago.  In  1885,  however,  a  new  turn  was  given  to  the 
subject  by  the  enunciation  of  the  modern  theory  of  solution 
by  van't  Hoff.  Many  of  the  experimental  facts  on  which  this 
theory  is  based  had  previously  been  established  by  the  work  of 
Ostwald,  Raoult  and  others,  and  these  results  were  correlated, 
and  many  fresh  avenues  opened  for  investigation,  by  van't  HofFs 
theory,  the  most  important  point  in  which  is  the  conception  of 
osmotic  pressure,  which  will  now  be  considered. 

It  has  already  been  shown  that  the  laws  applicable  to  gases 
are  very  simple  and  that  these  laws  are  most  strictly  followed  in 
the  rarefied  condition  ;  on  the  molecular  theory  this  is  accounted 
for  by  assuming  that  the  particles  are  then  so  far  apart  as  to 
exert  little  or  no  mutual  influence,  and  that  the  space  filled  by 
the  material  of  the  particles  is  negligible  in  comparison  with 
the  space  occupied.  Similarly,  we  may  reasonably  anticipate 
that  the  laws  expressing  the  behaviour  of  dissolved  substances 
will  be  most  simple  in  dilute  solution,  in  other  words,  when 
one  of  the  components  (the  solvent)  is  present  in  large  propor- 
tion compared  with  the  other  (the  solute),  and  this  is  quite 
borne  out  by  the  facts. 

Osmotic  Pressure.  Semi-permeable  Membranes— 
When  a  few  drops  of  bromine  are  carefully  placed  by  means 
7  97 


98          OUTLINES  OF  PHYSICAL  CHEMISTRY 

of  a  pipette  at  the  bottom  of  a  jar  full  of  hydrogen  or  air,  and 
the  jar  is  covered  and  allowed  to  stand,  it  will  be  found  after 
some  time  that  the  heavy  bromine  vapour  has  distributed  itself 
uniformly  throughout  the  confined  space  against  the  force  of 
gravity.  We  may  say  that  the  bromine  vapour  exerts  a  pressure 
in  virtue  of  which  it  diffuses  into  those  parts  of  the  confined 
space  where  the  pressure  is  less,  and  equilibrium  is  only  attained 
when  the  pressure  is  equal  throughout.  In  an  exactly  similar 
way,  if  a  sugar  solution  is  carefully  covered  with  a  layer  of 
water,  the  dissolved  sugar  exerts  a  pressure  with  the  result  that 
it  ultimately  becomes  uniformly  distributed  in  the  solution. 
This  pressure  cannot  be  determined  directly,  since  the  external 
pressure  is  the  sum  of  this  and  the  pressure  of  the  liquid,  but 
the  principle  of  the  method  used  for  measuring  it  will  be  under- 
stood from  its  analogy  with  the  method  already  described 
for  measuring  the  partial  pressure  of  a  gas  in  a  mixture  (p.  81). 
In  the  latter  case,  it  will  always  be  possible  to  determine  the 
partial  pressure  of  a  gas,  A,  mixed  with  another  gas,  B,  when  a 
membrane  is  known  which  allows  B,  but  not  A,  to  pass  through. 
Such  a  membrane  is  said  to  be  semi-permeable,  and  for  a 
mixture  of  nitrogen  and  hydrogen  heated  palladium  answers 
the  purpose.  It  is  clear  that,  if  we  could  find  a  membrane 
which  allows  water,  but  not  dissolved  sugar,  to  pass  through, 
the  pressure  exerted  by  the  latter  in  solution,  its  so-called 
osmotic  pressure,  could  be  measured. 

Such  membranes  were  discovered  by  Traube,  in  the  course 
of  his  experiments  on  so-called  artificial  vegetable  cells.  The 
most  suitable  membrane  for  the  purpose  was  found  to  be  copper 
ferrocyanide,  and  the  formation  of  this  membrane  and  its  im- 
permeability for  certain  dissolved  salts  may  be  illustrated  as 
follows.  A  glass  tube,  provided  with  a  rubber  tube  and  clip 
at  one  end  and  open  at  the  other,  is  partly  filled  by  suction 
with  an  aqueous  solution  of  copper  acetate  (about  2'8  per  cent.) 
and  ammonium  sulphate  (0-5  per  cent.),  and  the  open  end, 
in  which  the  surface  of  the  liquid  has  been  made  parallel  by 


DILUTE  SOLUTIONS 


99 


adjustment,  is  then  dipped  carefully  into  a  2-4  per  cent,  aqueous 
solution  of  potassium  ferrocyanide,  containing  a  little  barium 
chloride,  and  the  tube  supported  in  that  position.  A  thin 
membrane  of  copper  ferrocyanide  forms  across  the  lower  end  of 
the  tube,  and  if  the  experiment  has  been  carefully  performed, 
it  will  be  found  that  even  after  standing  some  hours  there  is 
no  white  precipitate  (of  barium  sulphate)  in  the  lower  solution, 
showing  that  the  membrane  is  impervious  to  ammonium  sul- 
phate. Traube  tried  many  other  membranes,  but  none  proved 
so  efficient  as  copper  ferrocyanide. 

Measurement  of  Osmotic  Pressure — The  semi-permeable 
membranes  prepared  by  Traube  were  much  too  weak  to  with- 
stand fairly  large  pressures,  and  their  use 
for  actual  measurements  was  only  ren- 
dered possible  by  Pfeffer's  idea  of  deposit- 
ing them  in  the  walls  of  a  porous  pot  A 
(Fig.  1 6)  such  as  are  used  for  experiments 
on  gas  diffusion.  The  pot  is  first  carefully 
washed,  soaked  in  water  for  some  time, 
then  nearly  filled  with  a  solution  of  copper 
sulphate  (2-5  grams  per  litre),  dipped 
nearly  to  the  neck  in  a  solution  of  potas- 
sium ferrocyanide  (2-1  grams  per  litre)  and 
allowed  to  stand  for  some  hours.  The 
salts  diffuse  through  the  walls  of  the  pot 
and  at  their  junction  form  a  membrane  of 
copper  ferrocyanide,  which,  since  it  is  im- 
permeable for  the  salts  from  which  it  is 
formed,  remains  quite  thin  but  is  capable 
of  withstanding  fairly  large  pressures, 
owing  to  its  being  supported  by  the  walls. 
The  cell  is  then  taken  out,  washed,  filled 

rlG.  io. 
with  a  strong  solution  of  sugar,  and  closed 

with  a  well-fitting  rubber  cork  through  which  an  open  glass  tube, 
B,  passes.  To  ensure  the  tightness  of  the  apparatus,  it  is  of 


-_Water_ 


ioo        OUTLINES  OF  PHYSICAL  CHEMISTRY 

advantage,  before  forming  the  membrane,  to  dip  the  upper  part 
of  the  pot,  to  the  depth  of  about  two  inches,  into  melted  paraffin, 
and  after  the  pot  is  filled  and  the  cork  and  tube  placed  in  position, 
the  upper  surface  should  be  covered  with  melted  paraffin.  When 
a  cell  thus  prepared  is  placed  in  water,  the  water  passes  in,  the 
pressure  inside  slowly  increases  (as  shown  by  the  rise  in  level 
of  the  solution  in  the  tube),  and  finally  reaches  a  point  at  which, 
when  the  cell  has  been  properly  prepared,  it  remains  constant 
for  days.  The  maximum  pressure  thus  attained,  in  other  words, 
the  excess  of  pressure  which  must  prevail  inside  the  cell  in  order 
to  prevent  more  water  flowing  in  through  the  semi-permeable 
membrane^  is  termed  the  osmotic  pressure  of  the  solution. 

In  accurate  measurements,  it  is  preferable  to  close  the  cell  with 
a  cork  carrying  a  closed  manometer,  containing  a  definite 
volume  of  air  confined  over  mercury.  Dilution  of  the  solution 
by  the  entry  of  a  large  volume  of  water  is  thus  avoided.  This 
arrangement  was  used  by  Pfeffer  in  his  original  experiments. 

The  osmotic  pressures  measured  in  this  way  are  very  con- 
siderable— thus  a  i  per  cent,  solution  of  cane  sugar  exerts  a 
pressure  of  more  than  half  an  atmosphere,  and  a  i  per  cent, 
potassium  nitrate  solution  over  two  atmospheres. 

The  question  as  to  the  relation  between  osmotic  pressure  and 
concentration  of  the  solution  was  investigated  by  Pfeffer,  and 
the  results  obtained  for  aqueous  solutions  of  sugar  and  of 
potassium  nitrate  at  room  temperature  are  given  in  the  ac- 
companying table,  in  which  C  represents  the  concentration  of 
the  solution  (in  grams  per  ioo  c.c.  of  solution)  and  P  the 
osmotic  pressure  (in  cm.  of  mercury). 

Cane  Sugar.  Potassium  Nitrate. 

C      P     P/C       C     P     P/C 

1  53'5    53*5       0-8     130-4    163 

2  101*6    50*8       1-43    218-5    153 
4     208-2    52-1       3-33    436-8    133 
6     307-S    Si'3 

It  is  clear  from  these  results  that  the  ratio  P/C  is  approximately 


DILUTE  SOLUTIONS  101 

constant  for  any  one  solution,  in  other  words,  the  osmotic  pres- 
sure of  a  solution  is  proportional  to  its  concentration.  It  will 
be  observed  that  the  ratio  is  somewhat  less  for  potassium  nitrate 
at  the  higher  pressures,  a  result  due  in  part  to  the  slight  per- 
meability of  the  membrane  for  the  salt  under  these  conditions. 

It  was  also  shown  by  Pfeffer  that  the  osmotic  pressure  at 
constant  concentration  increases  with  the  temperature ;  some 
of  the  results  obtained  in  this  connection  are  quoted  on  the  next 
page. 

The  magnitude  of  the  osmotic  pressure  observed  with 
different  membranes  was  not  quite  the  same,  but  this  must 
be  ascribed  to  the  imperfection  of  most  of  the  membranes, 
as  it  can  be  shown  theoretically  that  the  numerical  value  of 
the  osmotic  pressure  is  independent  of  the  nature  of  the 
membrane,  provided  the  latter  is  perfectly  semi-permeable. 

Yan't  Hoff's  Theory  of  Solutions — Pfeffer's  investiga- 
tions were  undertaken  for  botanical  purposes,  and  their  great 
general  importance  was  only  recognised  in  1885  by  van't  Hoff, 
who  used  them  as  the  experimental  basis  of  a  new  theory  of 
solution.  We  have  already  seen  that  osmotic  pressure  may  be 
regarded  as  in  some  respects  analogous  to  gas  pressure,  and  as 
the  former  can  be  measured  as  described  in  the  previous  section 
we  are  now  in  a  position,  following  van't  HofT,  to  investigate 
the  relationship  between  osmotic  pressure,  volume  and  tem- 
perature as  has  already  been  done  for  gases. 

As  regards  the  relation  between  osmotic  pressure  and  volume 
at  constant  temperature,  we  have  seen  in  the  previous  section 
that  P/C  is  constant  for  any  one  substance,  and  as  the  concen- 
tration is  inversely  as  the  volume  in  which  a  definite  weight  of 
substance  is  dissolved,  we  obtain,  by  substituting  i/V  for  C, 
the  equation  PV  =  constant,  the  exact  analogue  for  solutions 
ot  Boyle's  law  for  gases. 

With  reference  to  the  relation  between  osmotic  pressure  and 
temperature  at  constant  concentration,  van't  HofT  showed  from 
Pfeffer's  observations  that  the  osmotic  pressure,  P,  like  the  gas 


102       OUTLINES  OF  PHYSICAL  CHEMISTRY 

pressure,  is  proportional  to  the  absolute  temperature,  T.  Some 
of  the  observations  on  which  this  conclusion  is  based  are  given 
in  the  accompanying  table  : — 

Cane  Sugar.  Sodium  Tartrate. 

/           T          P  t           T           P 

14*2°     287*2     51*0  I3'3°     285*3°     9°'8 

32-0°     305-0     54-4  (54-6)  37-0°     310-0°     98-3  (98-2) 

The  observed  values  are  given  in  the  third  column,  with  the 
calculated  values  in  brackets ;  the  agreement  is  within  the  limits 
of  experimental  error. 

From  these  two  equations,  PV  =  const,  and  P  ex  T,  we  can 
derive  an  equation  for  dilute  solutions  corresponding  to  that 
already  obtained  for  gases  (p.  26), 

PV  =  rT, 

in  which  P  represents  the  osmotic  pressure  of  a  solution  con- 
taining a  definite  weight  of  a  solute  in  the  volume,  V,  of  solution, 
and  r  is  a  constant. 

It  remains  to  calculate  the  numerical  value  of  r  for  a  definite 
amount,  say  a  mol  of  a  dissolved  substance,  as  has  already  been 
done  for  gases.  This  can  readily  be  done  from  Pfeffer's  observa- 
tion that  a  i  per  cent,  solution  of  cane  sugar  at  o°  exerts  an 
osmotic  pressure  of  49*3  cm.  of  mercury.  The  molecular 
weight  of  cane  sugar  is  342,  the  volume  in  which  it  is  contained 
34,200  c.c.,  the  pressure  is  49*3  x  13*59  gram/cm.2,  and  the 
absolute  temperature  273°.  Hence 

PV       4Q--*  x  i  v^Q  x  14,200 
r  =  —  =  3212 as*  -   =  83,900  (in  gram-cm,  units), 

/  O 

a  value  which  almost  exactly  corresponds  with  that  obtained 
for  gases.  As  the  same  value  for  r  is  obtained  for  a  mol  of 
other  organic  compounds,  such  as  urea  and  glucose,  we  will 
represent  it  by  R,  to  indicate  that  it  is  a  factor  of  general  im- 
portance. We  have  thus  obtained  two  results  of  the  greatest 
importance :  (i)  the  equation  PV  =  RT  is  valid  for  dilute  solu- 


DILUTE  SOLUTIONS  103 

tions ;  (2)  the  numerical  value  of  R  is  the  same  for  dissolved 
substances  as  for  gases.  The  latter  statement  implies,  as  is 
clear  from  the  general  equation,  that  the  osmotic  pressure  of  a 
definite  quantity  of  cane  sugar  or  other  substance  in  solution  is 
equal  to  the  gas  pressure  which  it  would  exert  if  it  occupied  the 
same  volume  in  the  gaseous  form.  We  may  therefore  say  with 
van't  Hoff  that  "  the  osmotic  pressure  exerted  by  any  substance 
in  solution  is  the  same  as  it  would  exert  if  present  as  gas  in  the 
same  volume  as  that  occupied  by  the  solution,  provided  that  the 
solution  is  so  dilute  that  the  volume  occupied  by  the  solute  is 
negligible  in  comparison  with  that  occupied  by  the  solvent". 
This  statement  holds  for  all  temperatures,  as  is  at  once  clear 
from  the  fact  that  the  solution  obeys  the  gas  laws.  Certain 
important  exceptions  to  the  above  rule,  more  particularly  in 
the  case  of  solutions  which  conduct  the  electric  current,  will  be 
discussed  in  a  later  chapter. 

Some  important  consequences  of  the  validity  of  the  general 
equation,  PV  =  RT,  for  dissolved  substances  will  be  dealt  with 
in  detail  later.  In  particular,  the  molecular  weight  of  a  dis- 
solved substance  is  the  quantity  in  grams  which,  when  dissolved 
in  22-4  litres  at  o°,  exerts  an  osmotic  pressure  of  i  atmosphere, 
a  definition  almost  exactly  analogous  to  that  for  gases  (p.  36). 
The  same  fact  may  be  expressed  somewhat  differently  as  fol- 
lows :  Quantities  of  different  substances  in  the  ratio  of  their 
molecular  weights,  when  dissolved  in  equal  volumes  of  the 
same  solvent,  exert  the  same  osmotic  pressure. 

So  far,  we  have  considered  only  the  experimental  basis  of  the 
theory  of  solution.  It  has,  however,  been  shown  theoretically 
by  van't  Hoff,  by  thermodynamical  reasoning,  that  the  osmotic 
pressure  and  gas  pressure  must  have  the  same  absolute  value, 
if  the  solution  is  sufficiently  dilute,  and  this  conclusion  has 
been  confirmed  by  Lord  Rayleigh  and  by  Larmor,  among 
others.  The  latter  writer  puts  the  matter  as  follows :  "  The 
change  of  available  energy  on  further  dilution,  with  which 
alone  we  are  concerned  in  the  transformations  of  dilute  solu- 


io4        OUTLINES  OF  PHYSICAL  CHEMISTRY 

tions  [cf.  p.  150],  depends  only  on  the  further  separation  of 
the  particles  .  .  .  and  so  is  a  function  only  of  the  number 
of  dissolved  molecules  per  unit  volume  and  of  the  temperature, 
and  is,  per  molecule,  entirely  independent  of  their  constitution 
and  that  of  the  medium,"  l  the  assumption  being  made  that 
the  particles  are  so  far  apart  that  their  mutual  influence  is 
negligible.  "The  change  of  available  energy"  is  thus  brought 
into  exact  correlation  with  that  which  occurs  in  the  expansion 
of  a  gas. 

Recent  direct  Measurements  of  Osmotic  Pressure — 
It  is  a  remarkable  fact  that,  although  Pfeffer's  osmotic  pres- 
sure measurements  were  made  as  early  as  1877,  the  degree  of 
accuracy  attained  by  him  has  not  been  improved  upon  until 
quite  recently.  Accurate  measurements  are,  however,  very 
desirable,  because  although  the  relation  between  osmotic  pres- 
sure and  concentration  can  be  calculated  from  the  gas  laws  in 
dilute  solution,  there  is  still  much  uncertainty  as  to  how  far  the 
gas  laws  are  applicable,  or  what  is  the  exact  relationship  between 
osmotic  pressure  and  concentration,  in  concentrated  solutions. 
In  particular,  it  is,  or  was  until  quite  recently,  uncertain  whether 
V  in  the  general  equation,  PV  =  RT,  should  represent  the  volume 
of  the  solvent  or  that  of  the  solution.  This  uncertainty  has 
been  to  some  extent  removed  by  the  very  careful  measurements 
carried  out  by  Morse  and  Frazer 2  since  1903  by  Pfeffer's  method 
with  slight  modifications.  Their  results  show  that,  if  V  in  the 
general  equation  be  taken  as  the  volume  of  the  solvent,  aqueous 
solutions  of  cane  sugar  approximately  follow  the  gas  laws  up  to 
a  concentration  of  342  grams  of  the  solute  in  1000  grams  of 
water.  A  few  of  their  results,  illustrating  the  above  statement, 
are  given  in  the  accompanying  table;  the  numbers  under 
"gaseous"  are  calculated  on  the  assumption  that  the  sub- 
stance as  gas  occupies  the  same  volume  as  the  solvent  in  the 
solution. 

aLarmor,  Encyc.  Britannica,  loth  ed.,  vol.  xxviii.,  p.  170. 

*Amer.  Chem.  ?.,  1905,34,  i;  1906,  36,  i,  39  J  1007,  37>  324,  425. 
558;  38,  175;  1908,  39,  667;  40,  i,  194;  1909,  41*  !>  257;  i9"»  45.  554. 
etc. 


DILUTE  SOLUTIONS 


105 


Concentration  of  Solution. 

Pressure  at 

constant  temp.           Ratio  of 

A. 

(20°)  (atn 

lospheres).             osmotic  nres- 

Mols  per  rooo  grams 
of  water. 

Mols  per  litre  o? 
solution. 

re  to  gas 
ressure. 

Gaseous. 

Osmotic.              p 

O*IO 

0-09794 

2-39 

2-522 

'OSS 

O"2O 

0*19192 

4-78 

5^23 

•051 

0*40 

0-36886 

9*56 

9-96 

•038 

o'6o 

0-53252 

14*34 

15*20 

•060 

0-80 

0-68428 

19*12 

20*6o 

•077 

I-OO 

0-82534 

23-90 

26*12 

•093 

The  table  shows  that  only  when  concentrations  are  referred  to 
a  definite  weight  (or  volume)  of  solvent  is  there  proportionality 
between  concentration  and  osmotic  pressure ;  if  they  are  re- 
ferred to  a  constant  volume  of  solution  ("column  2)  the  osmotic 
pressure  increases  faster  than  the  concentration.  The  numbers 
in  the  fifth  column  show,  however,  that  the  osmotic  pressure 
at  20°  is  on  the  average  about  6  per  cent,  greater  than  the 
gas  pressure.  Curiously  enough,  the  ratio  is  about  the  same 
at  all  temperatures  from  o°  to  25°. 

Other  Methods  of  Determining  Osmotic  Pressure — The 
difficulties  inherent  in  the  direct  determination  of  osmotic 
pressure  can  often  be  avoided  by  determining  it  indirectly 
by  comparison  with  a  solution  of  known  osmotic  pressure. 
Solutions  which  have  the  same  osmotic  pressure  are  said  to 
be  isotonic  or  isosmotic. 

One  such  method,  used  by  de  Vries,  depends  on  the  use 
of  plant  cells  as  semi-permeable  membranes.  The  protoplasmic 
layer  which  surrounds  the  cell-sap  is  permeable  to  water,  but 
impermeable  to  many  substances  dissolved  in  the  cell-sap,  such 
as  glucose  and  potassium  malate.  If  such  a  cell  is  placed  in 
contact  with  a  solution  of  higher  osmotic  pressure  than  the 
cell-sap,  water  is  withdrawn  from  the  cell  (just  as  a  sugar 
solution  absorbs  water  through  a  semi-permeable  membrane) 
and  the  protoplasm  shrinks  away  from  the  cell-wall ;  a  pheno- 
menon which  is  termed  plasmolysis.  If,  however,  the  solution 
has  a  smaller  osmotic  pressure  than  that  of  the  cell-sap,  water 
enters  the  cell,  the  protoplasm  expands  and  lines  the  cell-wall. 
The  behaviour  of  the  protoplasm,  especially  if  coloured,  can  be 
1  Zeitsch.  physikal,  Chem.,  1888,  2,  415. 


io6       OUTLINES  OF  PHYSICAL  CHEMISTRY 

followed  under  the  microscope,  and  by  trial  a  solution  can  be 
found  which  has  comparatively  little  effect  upon  the  appearance 
of  the  cell,  and  is  therefore  isotonic  with  the  cell  contents. 

A  method  depending  on  the  same  principle,  in  which  red 
blood  corpuscles  are  used  instead  of  vegetable  cells,  has  been 
described  by  Hamburger,1  and  the  cell-walls  of  bacteria  may 
also  be  used  as  semi-permeable  membranes. 

The  following  table  contains  some  "  isotonic  coefficients  "  as 
given  by  de  Vries  and  by  Hamburger ;  the  numbers  represent 
the  ratio  of  the  osmotic  pressures  of  equimolecular  or  equimolar 
solutions  of  the  compounds  mentioned. 

Isotonic  Coefficients. 

Plasmolytic  With  Red  Blood 

Substance.                          Method.  Corpuscles. 

Cane  sugar    .         .         .1-81  1*72 

Potassium  nitrate   .         .3*0  3-0 

Sodium  chloride     .              3*0  3'o 

Calcium  chloride    .         .     4*33  4*05 

It  will  be  observed  that,  although  the  results  obtained  by  the 
two  methods  agree  fairly  well,  the  osmotic  pressures  for  equi- 
valent solutions  are  not  equal,  as  would  be  expected  according 
to  Avogadro's  hypothesis.  The  deviation  from  the  expected 
result  is  such  that  potassium  nitrate,  for  example,  exerts  an 
osmotic  pressure  about  1*7  times  greater  than  that  due  to  an 
equimolar  solution  of  cane  sugar.  This  observation  is  of 
fundamental  importance  in  connection  with  modern  views  as 
to  salt  solutions. 

The  Mechanism  of  Osmotic  Pressure— The  foregoing 
considerations  are  quite  independent  of  any  hypothesis  as  to 
the  exact  nature  of  osmotic  pressure,  and  so  far  no  general 
agreement  has  been  reached  on  this  point.  Van't  Hoff  inclines 
to  the  view  that  the  pressure  is  to  be  accounted  for  on  kinetic 
grounds,2  perhaps  as  being  due  to  the  bombardment  of  the 

1  Zeitsch.  physikal.  Chem.,  1890,  6,  319. 

2  For  a  discussion  between  van't  Hoff  and  Lothar  Meyer  on  this  point, 
see  Zeitsch.  physikal.  Chem.,  1890,  5,  23,  174. 


DILUTE  SOLUTIONS 


107 


u 


walls  of  the  vessel  by  solute  particles,  in  the  same  way  as  the 
pressure  of  a  gas  is  produced  according  to  the  kinetic  theory, 
and  the  fact  that  the  osmotic  pressure  is  proportional  to  the 
absolute  temperature  appears  rather  to  support  this  suggestion. 
Other  views  are  that  it  is  connected  with  attraction  between 
solvent  and  solute,  or  perhaps  with  surface  tension  effects.  It 
may  be  pointed  out  that  the  equivalence  of  osmotic  pressure 
Lind  gas  pressure  in  great  dilution  is  no  evidence  that  they  arise 
from  the  same  cause. 

As  regards  semi-permeable  membranes,  their  efficiency  does 
not  depend,  as  might  at  first  sight  be  sup- 
posed, on  anything  in  the  nature  of  a 
sieve  action,  only  the  smaller  molecules 
being  allowed  to  pass,  but  rather  upon  a 
difference  in  their  solvent  power  for  the  two 
components  of  the  mixture.  The  action 
of  the  palladium  in  Ramsay's  experiment 
(p.  81)  is  very  probably  to  be  accounted 
for  in  this  way,  and  that  the  same  is  true 
for  solutions  is  well  illustrated  by  an  in- 
structive experiment  due  to  Nernst  and 
illustrated  in  Fig.  17.  The  wide  cylin- 
drical glass  tube  A  is  closed  at  the  bottom 
with  an  animal  membrane  (bladder)  which 
has  previously  been  thoroughly  soaked  in 
water;  it  is  then  filled  with  a  mixture 
of  ether  and  benzene  and  fitted  with  a 
cork  and  narrow  tube,  as  shown  in  the  figure.  The  cell  is 
supported  on  a  piece  of  wire  gauze  in  a  beaker  partly  filled  with 
moist  ether  and  loosely  closed  by  a  cork,  B.  After  a  time  it 
will  be  observed  that  the  liquid  has  risen  to  a  considerable 
height  in  the  narrow  tube.  What  occurs  in  this  case  is  that 
the  ether  dissolves  in  the  water  with  which  the  membrane  is 
soaked,  and  in  this  way  is  transferred  inside  the  cell,  whilst 
the  benzene,  being  insoluble  in  water,  is  unable  to  pass  out. 


FIG.  17. 


io8       OUTLINES  OF  PHYSICAL  CHEMISTRY 

Similarly,  the  efficiency  of  the  copper  ferrocyanide  membrane 
may  depend  on  its  solvent  power  for  water  but  not  for 
sugar. 

Osmotic  Pressure  and  Diffusion — It  has  already  been 
pointed  out  that  there  is  a  close  connection  between  osmotic 
pressure,  as  defined  above,  and  diffusion ;  it  is  the  difference 
in  the  osmotic  pressure  of  cane  sugar  in  different  parts  of  a 
system  which  causes  it  in  time  to  be  uniformly  distributed 
through  that  system.  The  diffusion  of  dissolved  substances 
was  very  fully  investigated  by  Graham,  but  the  general  law  of 
diffusion  was  first  enunciated  by  Pick.  Fick's  law  is  comprised 
in  the  equation 

*  -  -  DA**, 

which  states  that  the  amount  of  solute,  ds,  which  passes  through 
the  cross-section  of  a  diffusion  cylinder  is  proportional  to  the 
area,  A,  of  the  cross-section,  to  the  difference  of  concentration, 
dc,  at  two  points  at  a  distance  dx  from  one  another,  to  the  time, 
dt,  and  to  a  constant,  D,  characteristic  for  the  substance,  and 
termed  the  diffusion-constant.  As  an  illustration  of  the  above 
formula,  it  was  found  that  when  dc=  i  gram  per  c.c.,  dx=i  cm., 
A=  i  sq.  cm.  and  ^/  =  one  day,  that  0*75  grams  of  sodium  chloride 
passed  between  the  two  surfaces.  This  is  excessively  slow,_in 
comparison  with  the  high  osmotic  pressures  set  up  even  by 
dilute  solutions,  and  the  explanation  is  to  be  found  in  the  great 
friction  due  to  the  smallness  of  the  particles.  As  the  driving 
force — the  osmotic  pressure — and  the  rate  of  diffusion  are 
known,  the  resistance  to  the  movement  of  the  particles  can  be 
obtained.  It  has  been  calculated  that  the  enormous  force  of 
four  million  tons  weight  is  needed  to  force  i  gram  mol  of  cane 
sugar  through  water  at  a  velocity  of  i  cm.  per  sec.  The  more 
rapid  diffusion  in  gases  may  plausibly  be  ascribed  to  the  much 
smaller  resistance  to  the  movement  of  the  particles. 

The  rate  of  diffusion  is    much   influenced  by  temperature 
and,  curiously  enough,  to  about  the  same  extent  for  all  solutes 


DILUTE  SOLUTIONS  109 

the  average  increase  is  about  ^  of  the  value  at  1 8°  for  every 
degree  C. 

MOLECULAR  WEIGHT  OF  DISSOLVED  SUBSTANCES. 

General — It  has  already  been  pointed  out  (p.  103)  that  since 
Avogadro's  hypothesis  is  valid  for  solutions,  the  molecular  weight 
of  a  dissolved  substance  can  readily  be  calculated  when  the 
osmotic  pressure  exerted  by  a  solution  of  known  concentration 
at  known  temperature  and  pressure  is  known.  An  illustration  of 
this  is  given  on  the  next  page.  As,  however,  the  direct  measure- 
ment of  osmotic  pressure  is  a  matter  of  considerable  difficulty, 
it  has  been  found  more  convenient  for  the  purpose  to  measure 
other  properties  of  solutions,  the  relationship  of  which  to  the 
osmotic  pressure  is  known.  The  only  three  methods  which  can 
be  dealt  with  here  are  : — 

(1)  The  lowering  of  vapour  pressure  ; 

(2)  The  elevation  of  boiling-point ; 

(3)  The  lowering  of  freezing-point, 

brought  about  by  adding  a  known  weight  of  solute  to  a  known 
weight  or  volume  of  solvent. 

It  can  be  shown  by  thermodynamical  reasoning  (p.  1 3 1)  that  un- 
der certain  conditions  the  lowering  of  vapour  pressure,  the  eleva- 
tion of  the  boiling-point  and  the  lowering  of  the  freezing-point  due 
to  the  addition  of  a  definite  quantity  of  solute  to  a  definite  volume 
of  solvent  are  each  proportional  to  the  osmotic  pressure  of  the 
solution.  Further,  the  equations  expressing  the  exact  relation- 
ships between  these  three  factors  and  the  osmotic  pressure  have 
also  been  established,1  and  all  these  theoretical  deductions  have 
been  fully  confirmed  by  experiment.  //  follows  that  just  as 
equimolecular  quantities  of  different  substances  in  equal  volumes 
of  the  same  solvent  exert  the  same  osmotic  pressure,  so  equimole- 
cular quantities  of  different  substances  in  equal  volumes  of  the 
same  solvent  raise  the  boiling-point,  lower  the  freezing-point,  and 
lower  the  vapour  tension  to  the  same  extent.  These  statements 
find  a  very  simple  representation  on  the  molecular  theory.  Since 
1  Appendix,  pp.  131-138. 


no       OUTLINES  OF  PHYSICAL  CHEMISTRY 

equimolecular  quantities  of  different  substances  contain  the 
same  number  of  molecules,  it  follows  that  the  magnitude  of 
the  osmotic  pressure,  lowering  of  vapour  pressure,  etc.,  depends 
only  on  the  number  of  particles  present  and  is  independent  of 
their  nature  (colligative  properties,  p.  63). 

The  molecular  weight  of  the  solute  could,  of  course,  be 
obtained  by  determining  one  of  the  factors  (i),  (2),  (3)  and 
then  calculating  the  value  of  the  osmotic  pressure,  but  it  is 
much  simpler  to  obtain  the  molecular  weight  by  comparison 
with  a  substance  of  known  molecular  weight. 

It  may  be  mentioned  that  besides  the  methods  just  indicated, 
there  are  other  analogous  methods  for  determining  molecular 
weights  which,  from  considerations  of  space,  cannot  be  referred 
to  here.  Nernst  has  pointed  out  that  any  process  involving  the 
separation  of  solvent  and  solute  can  be  used  for  determining 
molecular  weights,  and  a  little  consideration  will  show  that 
the  four  methods  just  mentioned  come  under  this  heading. 
Moreover,  the  osmotic  effect  of  the  solute  is  to  diminish  the 
readiness  with  which  part  of  the  solvent  may  be  separated  from 
the  solution,  and  the  effect  of  the  solute  on  the  boiling-  and 
freezing-points  of  the  solvent  must  therefore  be  in  the  direction 
already  indicated.  The  mathematical  proof  of  the  connection 
between  these  four  properties  depends  upon  the  equivalence  of 
the  work  done  in  removing  part  of  the  solvent  from  the  solu- 
tion (Appendix). 

The  four  different  methods  for  determining  molecular  weights 
in  solution  and  the  general  nature  of  the  results  obtained  will 
now  be  considered  in  detail. 

Molecular  Weights  from  Osmotic  Pressure  Measure- 
ments, (a)  from  absolute  values  of  the  osmotic  pressure — The 
principle  of  this  method  has  already  been  discussed  (p.  103). 
If  g  grams  of  substance,  dissolved  in  v  c.c.  of  solvent,  gives  an 
osmotic  pressure  of  /  cm.  at  T°  abs.,  the  molecular  weight, 
m,  will  be  that  quantity  which,  when  present  in  22,400  c.c.  of 
solvent,  will  give  an  osmotic  pressure  of  76  cm.  Hence,  since 
pvjT  is  proportional  to  the  amount  of  substance  used  (p.  26), 


DILUTE  SOLUTIONS  m 

pv  22,400  x  76 

s-  ^Tt  •  -ffj- 

g  x  22,400  x  76  x  (273  +  /°) 

«— -         -^r- 

As  an  example,  we  will  take  an  experiment  of  Morse  and  Frazer  (p.  105) 
in  which  a  solution  containing  34-2  grams  of  sugar  in  1000  c.c.  (really 
looo  grams)  of  water  gave  an  osmotic  pressure  of  2*522  atmospheres  = 
191*6  cm.  at  20°.  Hence 

m  =  34'2  x  22,400  x  76  x  293  = 

273  x  191-6  x  1000 
as  compared  with  the  theoretical  value  of  342. 
Alternatively,  by  formula  (2)  p.  36 

m  =  gRT-342  x  0*08205  *  293  =  326 
pv  2-522  x  i 

(b)  By  comparison  of  osmotic  pressures — Since  equimolecular 
solutions  in  the  same  solvent  have  the  same  osmotic  pressure, 
it  is  only  necessary  to  find  the  strengths  of  two  solutions  which 
are  in  osmotic  equilibrium  (isotonic),  and  if  the  molecular  weight 
of  one  solute  is  known  that  of  the  other  can  be  calculated. 
De  Vries  found  that  a  3-42  per  cent,  solution  of  cane  sugar 
was  isotonic  with  a  5-96  per  cent,  solution  of  raffinose,  the 
molecular  weight  of  which  was  then  unknown.  If  it  be  re- 
presented by  x,  then  3*42  :  5*96  :  :  342  :  :  x,  whence  #  =  596. 
This  result  has  since  been  confirmed  by  chemical  methods. 

Lowering  of  Vapour  Pressure — It  has  long  been  known 
that  the  vapour  pressure  of  a  liquid  is  diminished  when  a  non- 
volatile substance  is  dissolved  in  it,  and  that  the  diminution  is 
proportional  to  the  amount  of  solute  added.  In  1887  Raoult, 
on  the  basis  of  a  large  amount  of  experimental  work,  established 
the  following  important  rule  :  Equimolecular  quantities  of  differ- 
ent substances,  dissolved  in  equal  volumes  of  the  same  solvent, 
lower  the  vapour  pressure  to  the  same  extent.  On  comparing 
the  relative  lowering  (i.e.,  the  ratio  of  the  observed  lowering  and 
the  original  pressure)  in  different  solvents,  the  same  observer 
discovered  another  important  rule,  which  may  be  expressed  as 
follows  :  The  relative  lowering  of  vapour  pressure  is  equal  to  the 
ratio  of  the  number  of  molecules  of  solute  and  the  total  number  of 


ii2          OUTLINES  OF  PHYSICAL  CHEMISTRY 

molecules  in  the  solution.  Putting  p^  and  pz  for  the  vapour 
pressures  of  solvent  and  solution  respectively,  the  rule  may  be 
put  in  the  form 

A-  A  =       n 

A  N  +  n 

in  which  n  and  N  represent  the  number  of  molecules  of  solute 
and  solvent  respectively,  In  order  to  illustrate  the  validity  of 
this  rule,  some  results  given  by  Raoult  are  quoted  in  the  ac- 
companying table  ;  the  relative  lowering  is  that  due  to  the 
addition  of  i  mol  of  solute  to  100  mols  of  the  various  sol- 
vents :  — 

Solvent.  H20         PC13          CS2         CC14         CH3I    (C2H5)2O  CH3OH 

Relative  lowering  0*0102    0*0108    0*0105    0*0105    0*0105    0*0096    0*0103 

The  results  agree  excellently  among  themselves,  and  fairly  well 
with  the  calculated  value,  i/ioi  =  0*0099. 

About  the  same  time  van't  Hoff  introduced  the  conception 
of  osmotic  pressure,  and  showed  by  a  thermodynamical  method 
that  the  relation  between  the  relative  lowering  of  vapour  pres- 
sure and  the  osmotic  pressure  is  given  by  the  equation 

P- 


where  M  =  molecular  weight  of  solvent,  in  the  form  of  vapour,  s 
is  its  density,  and  the  other  symbols  have  their  usual  significance. 
The  expression  M/j-RT  is  therefore  constant,  since  it  depends 
only  on  the  nature  of  the  solvent,  and  consequently  the  relative 
lowering  of  vapour-pressure  is  proportional  to  the  osmotic  pres- 
sure P.  By  using  the  general  equation,  PV  =  «RT  (where  n  is 
the  number  of  mols  of  solute),  P  in  equation  (i)  can  be  elimin- 
ated,1 and  we  finally  obtain 

•DTP 

1  P  =  ~^7~,  where  V  is  the  volume  of  the  solvent.  If  N  represents 
the  number  of  mols  of  solvent,  M  its  molecular  weight  and  5  its 
density,  the  volume  V  of  the  solvent  =  MN/s.  Hence  P  =  -^^  »  and 
when  this  value  is  substituted  in  equation  (i)  we  obtain  (^  -/>2)  //>x  =  w/  N. 


DILUTE  SOLUTIONS  "3 

A -A  _  J? 

A      "  N- 

This  equation  differs  from  that  of  Raoult  in  that  the  de- 
nominator on  the  right-hand  side  is  N  instead  of  N  -f  n,  but 
they  become  identical  "  at  infinite  dilution  "  when  the  volume 
of  the  solute  is  negligible  in  comparison  with  that  of  the  solvent. 
By  substituting  for  n  and  N  g/m  and  W/M,  where  g  and  W 
are  the  weights  of  solute  and  solvent  respectively,  m  is  the 
(unknown)  molecular  weight  of  the  solute  and  M  that  of  the 
solvent  in  the  form  of  vapour,  we  obtain  the  equation 

A^A  __^M 

pl        ~  Wm 

which  enables  us  to  calculate  the  molecular  weight  of  a  dissolved 
substance  when  the  relative  lowering  produced  by  a  known 
weight  of  solute  in  a  known  weight  of  solvent  is  known.  As 
an  illustration,  an  experiment  of  Smits  may  be  quoted.  He 
found  that  at  o°  the  lowering  of  vapour  pressure  produced  by 
adding  29-0358  grams  of  sugar  to  1000  grams  of  water  is 
0-00705  mm.,  the  vapour  pressure  of  water  at  that  temperature 
being  4*62  mm.  Hence 

0-00701;        20-0^8  x   18 

r_*  =     *    33          _}  and  m  =  3   2 

4-62  looom 

in  exact  agreement  with  the  theoretical  value. 

As  the  lowering  of  vapour  pressure  is  very  small  and  not 
very  easy  to  determine  accurately  by  a  statical  method,  it  has 
not  been  very  largely  used  for  molecular  weight  determinations, 
the  closely  allied  method  depending  on  the  elevation  of  the 
boiling-point  being  preferred.  It  has,  however,  one  great 
advantage,  inasmuch  as,  unlike  the  boiling-point  and  freezing- 
point  methods,  it  can  be  used  for  the  same  solution  at  widely 
different  temperatures.  For  this  purpose,  a  dynamical  method 
suggested  by  Ostwald  and  worked  out  by  Walker l  has  certain 
advantages.  A  current  of  air  is  drawn  in  succession  through 
(x)  a  set  of  Liebig's  bulbs  containing  the  solution  of  vapour 

1  Zeitsch.  physikal.  Chem.,  1888,  2,  602. 
8 


ii4        OUTLINES  OF  PHYSICAL  CHEMISTRY 

pressure p^  (2)  similar  bulbs  containing  the  pure  solvent  vapour 
pressure  p^  (3)  a  U-tube  containing  concentrated  sulphuric 
acid.  In  the  first  set  of  bulbs  it  becomes  saturated  up  to 
p^  with  the  vapour  of  the  solvent,  in  the  second  set  up  to/lf  in 
the  U-tube  the  moisture  is  completely  absorbed.  The  loss  of 
weight  in  the  second  set  of  bulbs  is  proportional  to  p^  -p.,,  and 
the  gain  in  the  U-tube  to/j  (cf.  p.  Qi).1 

Elevation  of  Boiling-point — A  little  consideration  shows 
that  there  is  a  close  connection  between  this  method  of  deter- 
mining molecular  weights  and  that  depending  on  the  lowering 
of  vapour  pressure.  A  liquid  boils  when  its  vapour  pressure 
is  equal  to  that  of  the  atmosphere.  The  presence  of  a  solute 
lowers  the  vapour  pressure,  and  to  reach  the  same  pressure 
as  before  we  require  to  raise  the  temperature  a  little ;  it  is 
evident  that,  to  a  first  approximation,  this  elevation  must  be 
proportional  to  the  lowering  of  vapour  pressure.  It  follows 
that,  in  this  case  also,  equimolecular  quantities  of  different 
solutes,  in  equal  volumes  of  the  same  solvent,  raise  the  boiling- 
point  to  the  same  extent.  The  molecular  weight  of  any  soluble 
substance  may  therefore  be  found  by  comparing  its  effect  on 
the  boiling-point  of  a  solvent  with  that  of  a  substance  of  known 
molecular  weight. 

For  this  purpose,  it  is  convenient  to  determine  the  molecular 
elevation  constant,  K,  for  each  solvent,  that  is,  the  elevation  of 
boiling-point  which  would  be  produced  by  dissolving  a  mol  of 
any  substance  in  100  grams  or  100  c.c.  of  the  solvent.  Actually, 
of  course,  the  elevation  is  determined  in  fairly  dilute  solution, 
and  the  value  of  the  constant  calculated  on  the  assumption  that 
the  rise  of  boiling-point  is  proportional  to  the  concentration. 
Then  the  weight  in  grams  of  any  other  compound  which,  when 
dissolved  in  100  grams  or  100  c.c.  of  the  solvent,  produces  a 
rise  of  K  degrees  in  the  boiling-point  is  the  molecular  weight. 

If  g  grams  of  substance,  of  unknown  molecular  weight,  m, 
dissolved  in  L  grams  of  solvent  raises  the  boiling-point  8 

1  A  modification  of  this  method  has  recently  been  used  by  Lord  Berkeley 
and  Hartley  for  the  indirect  determination  of  the  osmotic  pressure  of  con- 
centrated solutions  of  cane  sugar  (Proc.  Roy.  Soc.,  1906,  77A,  156. 


DILUTE  SOLUTIONS  115 

degrees,  whilst  m  grams  in   100  grams  of  solvent  give  a  rise 
of  K  degrees,  it  follows  that 

*  TS      ^ 

:  8  :  :  m  :  :  K,  whence  m  =  —  - 


-=-      . 
Ld 

In  the  course  of  the  last  few  years,  the  constants  for  100  grams 
and  100  c.c.  have  been  very  carefully  determined  for  a  large 
number  of  solvents,  and  some  of  the  more  important  data  are 
given  in  the  accompanying  table  :  — 


Solvent. 

IVlUlCCUlcU     A^lCVc 

100  grams. 

IL1U11    l*UUDU 

100  C.C. 

Water 

5'2 

5*4 

Alcohol 

n'5 

IS'6 

Ether 

2I*O 

30'3 

Acetone 

.       16-7 

22'2 

Benzol 

26*7 

32-8 

Chloroform 

.       39-0 

277 

Pyridine 

.       30*1 

Van't  Hoff  has  shown  that  these  constants,  some  of  which 
had  previously  been  obtained  empirically  by  Raoult,  can  be 
calculated  from  the  latent  heat  of  vaporization,  H,  per  gram  of 
solvent,  and  its  boiling-point,  T,  on  the  absolute  scale,  by 
means  of  the  formula 

_   0-02T2 

~H~ 

As  an  example,  the  calculated  value  for  the  molecular  elevation 
constant  for  water,  the  latent  heat  of  vaporization  of  which  at 
its  boiling-point  is  537  calories,  is 

K  =  (0-02  x  (373)2)/537  =  5'* 

in  satisfactory  agreement  with  the  experimental  value.  For  all 
solvents  which  have  been  carefully  investigated,  the  experi- 
mental and  calculated  values  are  in  good  agreement.1 

1  The  observed  and  calculated  values  for  a  large  number  of  solvents 
are  given  in  Landolt  and  Bernstein's  tables. 


n6         OUTLINES  OF  PHYSICAL  CHEMISTRY 

Experimental  Determination  of  Molecular  Weights 
by  the  Boiling-point  Method — The  ease  and  certainty 
with  which  such  determinations  can  now  be  made  is  largely 
due  to  the  work  of  Beckmann.  One  of  the  methods  sug- 
gested by  him  will  first  be  considered,  and  then  a  method 
due  to  Landsberger,  based  on  a  different  principle. 

(a)  Beckmann  s  Method — The  apparatus  used  is  represented 
in  Fig.  1 8.  The  boiling-tube,  A,  is  provided  with  two  side 
tubes,  /!,  by  means  of  which  the  solute  (solid  or  liquid)  is 
introduced,  and  /2,  which  is  connected  to  a  small  condenser, 
by  the  action  of  which  the  amount  of  solvent  is  kept  fairly 
constant.  The  solution  is  made  to  boil  by  the  heat  from  a 
small  screened  burner,  B,  which  can  be  carefully  regulated, 
and  the  boiling  liquid  is  insulated  by  means  of  an  air  jacket 
between  the  outer  cylindrical  glass  tube,  G,  and  the  boiling 
tube.  As  the  temperature  of  the  vapour  which  escapes  from 
a  boiling  solution  is  little,  if  any,  above  the  boiling-point  of  the 
pure  solvent,  it  is  necessary  to  place  the  thermometer  in  the 
boiling  liquid  so  that  the  bulb  is  completely  immersed.  The 
liquid  tends  to  become  superheated,  and  to  eliminate  this  source 
of  error  Beckmann  recommends  filling  up  the  boiling-tube 
nearly  to  the  level  of  the  liquid  with  glass  beads  or  garnets,  or, 
still  better,  with  platinum  tetrahedra.  The  thermometer  repre- 
sented in  the  figure,  which  was  specially  designed  by  Beck- 
mann for  this  work,  has  a  large  bulb  and  an  open  scale, 
covering  only  5°-6°,  and  graduated  in  TJ<j°.  To  render  the 
thermometer  available  for  widely  different  temperatures,  there 
is  an  arrangement  by  means  of  which  the  amount  of  mercury 
in  the  bulb  can  be  so  adjusted  that  the  top  of  the  thread  can 
be  brought  on  the  scale  at  any  desired  temperature.  The  sol- 
vent, of  which  10  to  15  grams  is  usually  sufficient,  is  measured 
with  a  pipette,  or  weighed  by  difference  in  the  boiling-tube 
itself ;  the  solute,  if  solid,  may  be  conveniently  introduced  in 
the  form  of  a  compressed  pastille  or,  if  liquid,  by  means  of  a 
bent  pipette.  The  boiling-point  of  the  solvent  is  determined 


DILUTE  SOLUTIONS 


117 


by  causing  it  to  boil  fairly  vigorously,  and  the  temperature  should 
remain  constant  within  0*01°  —  o'oi5°  for  about  twenty  minutes 


FIG.  18. 


while  readings  are  being  taken.    The  temperature  is  then  allowed 
to  fall  several  degrees  by  removing  the  source  of  heat,  the  solute 


u8          OUTLINES  OF  PHYSICAL  CHEMISTRY 

rapidly  introduced,  the  boiling-point  again  determined,  a  fresh 
quantity  of  solvent  introduced,  the  boiling-point  re -determined, 
and  so  on.  The  thermometer  should  be  tapped  before  each 
reading.  The  amount  of  solute  added  may  conveniently  be 
such  that  the  boiling-point  is  raised  o-i5°-o"2°  after  each  addi- 
tion. It  may  be  pointed  out  that  more  satisfactory  results  are 
usually  obtained  when  differences  produced  by  the  addition  of 
more  solute  are  used  in  the  calculation  than  when  differences 
in  the  boiling-point  of  solvent  and  solution  are  used. 

As  an  illustration  of  the  calculation  of  the  results,  an  experi- 
ment with  camphor  in  ethyl  alcohol  may  be  quoted.  The 
addition  of  0-56  grams  of  camphor  to  16  grams  of  the  solvent 
raised  its  boiling-point  0-278°.  Hence 

loo^K       100  x  0-56  x  1 1 -5 
~L8~  16  x  0-278 

the  theoretical  value  for  C10H16O  being  142. 

With  proper  precautions,  the  results  obtained  by  this  method 
are  accurate  within  3-4  per  cent. 

(b)  Landsberger 's  Method — This  method  depends  upon  the 
fact  that  a  solution  can  be  heated  to  its  boiling-point  by  passing 
into  it  a  stream  of  the  vapour  of  the  boiling  solvent.  In  this 
case  there  is  little  or  no  risk  of  superheating,  as  the  temperature 
of  the  vapour  is  lower  than  the  boiling-point  of  the  solution. 
The  boiling-point  of  the  solvent  is  first  determined  by  passing  in 
vapour  till  the  temperature  ceases  to  rise,  some  of  the  solute 
is  then  added,  and  more  vapour  passed  in  until  the  boiling- 
point  of  the  solution  is  reached.  As,  during  the  heating,  the 
amount  of  solvent  increases  by  condensation  of  vapour,  the 
final  amount  of  solution,  upon  which  of  course  the  observed 
boiling-point  depends,  is  obtained  by  weighing  after  the  experi- 
ment. If  no  great  accuracy  is  required,  the  final  volume  may 
be  read  off  in  the  boiling-tube,  graduated  for  the  purpose. 
Radiation  may  be  minimised  by  jacketing  the  inner  tube  with 
the  vapour  of  the  boiling  solvent. 


DILUTE  SOLUTIONS  119 

Depression  of  the  Freezing-point — This  is  the  most 
accurate  and  most  largely  employed  method  for  the  deter- 
mination of  molecular  weights  in  solution.  The  two  necessary 
conditions  for  its  applicability  are  (i)  the  pure  solvent,  free  from 
any  of  the  solute,  must  separate  out  when  the  freezing-point  is 
reached ;  (2)  only  a  little  of  the  solvent  must  have  separated 
when  the  measurement  is  taken,  otherwise  the  concentration 
of  the  solution  will  be  appreciably  altered.  As  in  solubility 
determinations,  we  are  dealing  with  an  equilibrium  (p.  84)  in 
this  case  between  ice  and  solution,  and  the  experimental  fact 
is  that  the  more  concentrated  the  solution  the  lower  is  the  tem- 
perature at  which  equilibrium  is  reached.  It  is  thus  evident 
that  if  a  large  amount  of  the  solvent  separates  in  the  solid  form, 
the  observed  freezing-point  is  the  temperature  of  equilibrium 
with  a  more  concentrated  solution  than  that  originally  prepared. 

In  this  case  also,  the  osmotic  pressure,  and  hence  the  mole- 
cular weight,  could  be  calculated  from  the  formula  connecting 
osmotic  pressure  and  depression  of  the  freezing-point  (p.  138),  but 
the  comparison  method  is  always  used.  Just  as  for  the  boiling- 
point  (p.  114)  the  molecular  freezing-point  depression ,  i.e.,  the 
depression  produced  by  dissolving  i  mol  of  solute  in  100  grams 
or  100  c.c.  of  the  solvent,  has  been  determined  for  a  large 
number  of  solvents,  and  some  of  the  more  important  data  are 
given  in  the  accompanying  table. 


Molecular  Depression. 

Solvent. 

100  grams.              100  c.c. 

Water 

.      18-5                     18-5 

Benzol 

•      50                        56 

Acetic  acid 

•     39                     4i 

Phenol 

•     74 

Naphthalene 

.     69 

The  molecular  depression,  K,  can  be  calculated  from  the 
latent  heat  of  fusion,  H,  of  the  solvent  and  its  freezing  point 
on  the  absolute  scale  by  means  of  the  expression. 


120         OUTLINES  OF  PHYSICAL  CHEMISTRY 


analogous  to  that  which  holds  for  the  boiling-point  elevation. 
Thus  for  water  we  have  K  =  (0*02  x  (273)2)/8o  =  i8'6. 

It  may  be  mentioned,  as  a  matter  of  historical  interest,  that 
the  experimental  values  for  K  obtained  with  solutions  of  cane 
sugar  by  Raoult,  Jones  and  others,  were  at  first  much  greater 
than  1  8-6,  but  the  careful  experiments  of  Abegg,  Loomis, 
Wildermann,  and  later  of  Raoult  himself  made  it  clear  that 
the  high  values  previously  obtained  were  due  to  experimental 
error,  and  that,  with  proper  precautions,  the  value  of  K  deduced 
on  the  basis  of  the  theory  of  solution  was  fully  confirmed  by 
experiment. 

If  g  grams  of  solute,  in  L  grams  of  solvent,  caused  a  depres- 
sion, A,  of  the  freezing-point  of  the  solvent,  the  molecular  weight 
of  the  solute  can  be  calculated  from  the  lormula 


which  exactly  corresponds  with  that  already  given  for  elevation 
of  boiling-point. 

Experimental  Determination  of  Molecular  Weights 
by  the  Freezing-point  Method  —  The  apparatus  which  is 
used  almost  exclusively  for  this  purpose  was  also  designed  by 
Beckmann,  and  is  shown  in  Fig.  19.  The  inner  tube,  A,  which 
contains  the  solvent,  has  a  side  tube  by  which  the  solute  may 
be  introduced,  and  is  provided  with  a  Beckmann  thermometer, 
D,  and  a  stirrer,  preferably  of  platinum.  The  remainder  of  the 
apparatus  consists  of  a  tube,  B,  rather  wider  than  A,  and  fitted 
into  the  loose  cover  of  the  large  beaker,  C,  which  contains  water 
or  a  freezing-mixture  (ice,  or  ice  and  salt),  the  temperature  of 
which  is  2-3°  below  the  freezing-point  of  the  solvent. 

In  making  an  experiment,  15-20  grams  of  the  solvent  are 
weighed  or  measured  into  the  tube,  A,  the  stirrer  and  ther- 
mometer are  put  in  place,  and  A  is  then  placed  in  the  wider 


DILUTE  SOLUTIONS 


121 


tube  B,  which  acts  as  an  air  mantle.  The  liquid  is  then  stirred 
continuously  and  the  thermometer  observed.  Owing  to  super- 
cooling, the  temperature  falls  below  the  freezing-point  of  the 
solvent,  but  as  soon  as  solid  begins  to 
separate,  it  rises  rapidly,  owing  to  the 
latent  heat  set  free,  and  the  highest 
temperature  observed  is  taken  as  the 
freezing-point  of  the  solvent.  The  tube 
is  then  removed  from  the  bath,  the  solid 
allowed  to  melt,  a  weighed  amount  of  the 
solute  added,  and  the  determination  of  the 
freezing-point  repeated.  A  further  por- 
tion of  solute  may  then  be  added,  and 
another  reading  taken.  With  some  sol- 
vents there  is  considerable  supercooling, 
and  as  this  would  be  a  source  of  error 
owing  to  separation  of  much  solvent  when 
solidification  finally  occurs,  a  small  par- 
ticle of  solid  solvent  is  added  to  start 
solidification  when  the  temperature  has 
fallen  1-2°  below  the  freezing-point. 

As  an  illustration  of  the  calculation  of 
the  results,  an  experiment  with  napthalene 
in  benzene  may  be  quoted.  The  addition 
of  0*142  grams  of  the  compound  to 
20*25  grams  of  the  solvent  lowered  the 
freezing-point  0*284°.  Hence 


ioo  x  0*142  x  51*2 


126 


AL  0*284  x  20*25 

as  compared  with  the   theoretical  value  FIG.  19'. 

128. 

Results  of  Molecular  Weight  Determinations  in  Solu- 
tion. General — The  most  important  result  of  the  numerous 
molecular  weight  determinations  of  dissolved  substances  which 


122       OUTLINES  OF  PHYSICAL  CHEMISTRY 

have  been  made  in  recent  years  is  that  in  general  the  molecular 
weight  in  dilute  solution  is  the  same  as  that  deduced  from  the  simple 
chemical  formula  of  the  solute,  as  based  on  vapour  density  deter- 
minations or  on  its  chemical  behaviour.  For  example,  the 
empirical  formula  of  naphthalene  is  C5H4,  and  since  one-eighth 
of  the  hydrogen  can  be  replaced,  the  simplest  chemical  formula 
must  be  C10H8,  and  the  molecular  weight  128.  Cryoscopic 
determinations  in  benzene  gave  a  value  126,  so  that  naphthalene 
is  present  as  simple  molecules  in  solution. 

The  Van't  HofT-Raoult  formulae  (p.  112)  on  which  the 
determination  of  molecular  weights  in  solution  depend,  have 
been  deduced  on  certain  assumptions  which  hold  only  for  dilute 
solutions,  and  it  is  of  the  utmost  importance  to  bear  in  mind 
that  there  is  no  a  priori  reason  why  they  should  give  trust- 
worthy results  for  concentrated  solutions.  The  question  as  to 
how  far  the  gas  laws  hold  for  concentrated  solution,  or  what 
modifications  are  necessary,  has  been  much  debated,  but  so  far 
no  definite  conclusions  have  been  arrived  at.  It  is  mainly  a 
matter  for  further  experiment.  It  has  already  been  shown 
(p.  105)  that  when  V  in  the  general  formula  is  taken  as  the 
volume  of  the  solvent,  the  normal  molecular  weight  is  obtained 
for  cane  sugar  up  to  very  high  concentrations  on  the  assumption 
that  the  gas  laws  are  valid  for  these  solutions.  The  same  is 
true  for  other  compounds,  more  particularly  in  organic  solvents, 
as  may  be  illustrated  by  the  values  obtained  by  Beckmann  for 
camphor  in  benzene1  (theoretical  value  152)  : — 

Concentration.     Value  of  m.  Concentration.      Value  of  m. 

0-411  144  12'n  149 

1-253  143  23-12  152 

2791  145  26-59  154 

5'897  M7 

The  observed  molecular  weights  depend  not  only  on  the  nature 
of  the  solute  and  on  the  concentration,  but  also  very  largely  on 
the  nature  of  the  solvent.  Examples  will  be  given  in  the  follow- 
ing pages  showing  that  in  certain  solvents  the  observed  mole- 
1  Concentration  in  grams  per  100  grams  of  benzene. 


DILUTE  SOLUTIONS 


123 


cular  weights  are  often  higher  than  those  deduced  from  the 
chemical  formula  of  the  solute.  The  solute  is  then  said  to  form 
complex  molecules  or  to  be  associated,  and  the  solvent  is  termed 
an  associating  solvent.  In  other  solvents,  on  the  contrary,  the 
molecular  weight  may  be  equal  to  or  less  than  that  deduced 
from  its  chemical  formula.  In  the  latter  case  the  solute  is  said 
to  be  dissociated,  and  the  solvents  in  question  are  termed 
dissociating  solvents. 

Abnormal  Molecular  Weights — In  order  to  illustrate  the 
results  of  molecular  weight  determinations  from  a  slightly  differ- 
ent point  of  view,  the  following  table  contains  the  values  for  the 
molecular  freezing-point  depression,  K,  for  three  typical  sol- 
vents, water,  acetic  acid  and  benzene.  The  data  are  mainly  due 
to  Raoult,  and  in  calculating  K  it  is  assumed  that  the  molecular 
weight  corresponds  with  the  ordinary  chemical  formula  of  the 
solute : — 


Solvent — Water. 
Solute.  K. 
Cane  sugar  i8'6 
Acetone  .  17*1 
Glycerol  .  17'! 
Urea  .  .  187 


HC1 


NaCl 


•  39'1 

•  35'8 

•  35-8 

•  36*° 


Solvent — Acetic  Acid. 
Solute.  K. 

Methyl  iodide .  38-8 
Ether  .  .  .  39-4 
Acetone  .  .  38*1 
Methyl  alcohol  357 

HC1.  .  .  .  17-2 
H2SO4  .  .  .18-6 
(CH3COO)2Mg  1 8- 2 


Solvent  —  Benzene. 

Solute. 

K. 

Methyl  iodide  . 

5°'4 

Ether     .     .     . 

497 

Acetone      .     . 

49*3 

Aniline  .     .     . 

46-3 

Methyl  alcohol 

25-3 

Phenol  .     .     . 

32-4 

Acetic  acid 

25-3 

Benzoic  acid 

This  very  instructive  table  shows  that,  for  all  three  solvents, 
there  are  two  sets  of  values  for  K,  one  of  which  is  approximately 
double  the  other.  The  question  now  arises  as  to  which  of 
these  are  the  normal  values,  obtained  when  the  solute  exists  as 
single  molecules  in  solution.  This  can  at  once  be  settled  by 
using  van't  Hoffs  formula,  K  =  (o'O2T2)/H  (p.  120),  and  we 
find  that  the  normal  depressions  are  18-6,  39-0  and  51-2  for 
water,  acetic  acid  and  benzene  respectively.  This  means  that 
acetic  acid,  phenol  and  some  other  compounds  dissolved  in 


i24        OUTLINES  OF  PHYSICAL  CHEMISTRY 

benzene  produce  only  half  the  depression,  in  other  words,  exert 
only  about  half  the  osmotic  pressure  that  would  be  expected  ac- 
cording to  their  formulae,  whilst  in  water  certain  acids  and  salts 
have  an  abnormally  high  osmotic  pressure.  The  osmotic  pressure 
of  certain  mineral  acids  in  acetic  acid  is  abnormally  low. 

On  the  molecular  theory,  an  abnormally  small  osmotic 
pressure  shows  that  the  number  of  particles  is  smaller  than  was 
anticipated.  The  experimental  results  can  be  satisfactorily 
accounted  for  on  the  view  that  acetic  acid  and  benzoic  acid 
exist  as  double  molecules  in  benzene  solution,  and  that  phenol 
is  polymerized  to  a  somewhat  smaller  extent.  This  explanation 
seems  the  more  plausible  inasmuch  as  acetic  acid  contains  com- 
plex molecules  in  the  form  of  vapour  (p.  41). 

It  is  mainly  compounds  containing  the  hydroxyland  cyanogen 
groups  which  are  polymerized  in  non -dissociating  solvents ;  in 
dissociating  solvents,  such  as  water  and  acetic  acid,1  these  com- 
pounds have  normal  molecular  weights. 

It  may  be  anticipated  that  the  molecular  complexity  of 
solutes  will  be  greater  in  concentrated  solutions,  and  the  avail- 
able data  appear  to  show  that  such  is  the  case.  The  results 
are,  however,  somewhat  uncertain,  inasmuch  as  in  concentrated 
solution  the  gas  laws  are  no  longer  valid  (p.  122). 

Solvents  such  as  benzene  are  sometimes  termed  associating 
solvents,  but  this  probably  does  not  mean  that  they  exert  any 
associating  effect.  There  is  a  good  deal  of  evidence  to  show 
that  the  substances  existing  as  complex  molecules  in  benzene 
and  chloroform  solution  are  complex  in  the  free  condition,  and 
that  the  complex  molecules  are  only  partly  broken  up  in 
so-called  associating  solvents. 

The  explanation  of  the  behaviour  of  solutes  in  water  is  by 
no  means  so  simple,  and  can  only  be  dealt  with  fully  at 
a  later  stage.  The  data  in  the  table  indicate  that  cane 
sugar,  urea,  acetone,  etc.,  are  present  as  single  molecules  in 
solution,  but  hydrochloric  acid,  potassium  nitrate,  etc.,  be- 
have as  if  there  were  nearly  double  the  number  of  molecules  to 

1  That  acetic  acid  is  in  some  cases  at  least  a  dissociating  solvent  is 
evident  from  the  fact  that  the  molecular  weight  of  methyl  alcohol  in  it  is 
almost  normal. 


DILUTE  SOLUTIONS  125 

be  anticipated  from  the  formulae.  When  van't  Hoff  put  forward 
his  theory  of  solutions  he  was  quite  unable  to  account  for  this 
behaviour,  and  contented  himself  with  putting  in  the  general 
gas  equation  a  factor,  /,  to  represent  the  abnormally  high  os- 
motic pressure,  so  that  for  salts  and  the  so-called  "  strong  " 
acids  and  bases  in  aqueous  solution  the  equation  became 
PV  =  iRT. 

The  factor  /can  of  course  be  obtained  for  aqueous  solutions  by 
dividing  the  experimental  value  of  the  molecular  depression  by 
the  normal  constant,  18*6,  so  that  for  potassium  nitrate,  for 
example,  i  =  35-8/18-6  =  1*92. 

Van't  Hoff  recalled  the  fact  that  ammonium  chloride,  in  the 
form  of  vapour,  exerts  an  abnormally  high  pressure,  which  is 
simply  accounted  for  by  its  dissociation  according  to  the  equa- 
tion NH4C1  =  NH3  +  HC1,  but  it  did  not  appear  that  the 
results  with  salts,  etc.,  could  be  explained  in  an  analogous  way. 
We  shall  see  in  detail  later  that  the  elucidation  of  the  signifi- 
cance of  the  factor  i  was  of  the  highest  importance  for  the 
further  development  of  the  theory  of  solution.  According  to 
our  present  views,  the  substances  which  show  abnormally  high 
osmotic  pressures  are  partially  dissociated  in  solution,  not  into 
ordinary  atoms,  but  into  atoms  or  groups  of  atoms  associated 
with  electrical  charges.  The  equation  representing  the  partial 
splitting  up  of  potassium  nitrate,  for  example,  may  be  written 

+       

KNO3  =  K  +  NO3,  which  indicates  that  the  solution  contains 

potassium  atoms  associated  with  positive  electricity,  and  an 
equal  number  of  NO3  groups,  associated  with  negative  elec- 
tricity. These  charged  atoms,  or  groups  of  atoms,  are  termed 
ions. 

Molecular  Weight  of  Liquids — Our  knowledge  as  to  the 
molecular  weight  of  pure  liquids  is  due  mainly  to  the  investi- 
gations of  Eotvos  (1886)  and  of  Ramsay  and  Shields  (1893), 
and  is  based  on  the  remarkable  rule,  discovered  by  Eotvos, 
that  the  rate  of  change  of  the  ""molecular  surface  energy  "  of  many 


126       OUTLINES  OF  PHYSICAL  CHEMISTRY 

liquids  with  temperature  is  the  same.  If  y  represents  the  sur- 
face tension  and  s  the  "  molecular  surface,"  the  rule  in  question 
may  be  written 


where  c  is  a  constant.1  The  molecular  surface,  s,  can  be  ex- 
pressed in  terms  of  readily  measurable  quantities  as  follows  : 
The  molecular  volume  of  any  liquid  is  represented  by  Mv 
where  M  is  the  molecular  weight  and  v  the  specific  volume. 
If  the  molecular  volume  is  regarded  as  a  cube,  one  edge  of 
the  cube  will  measure  (Mvfi,  and  the  area  of  one  side  of  it 
(Mz/)3.  (Mz/)f  may  therefore  be  called  the  molecular  sur- 
face, s,  and  just  as  the  relative  molecular  volumes  of  different 
liquids  contain  an  equal  number  of  molecules  so  the  relative 
molecular  surfaces  for  different  liquids  are  such  that  an  equal 
number  of  molecules  lie  on  them.  Equation  (i)  then  becomes 

^  or 


dt 

1  The  student  should  make  himself  familiar  with  this  method  of  repre- 
senting rate  of  change,  as  it  is  largely  used  in  physical  chemistry.  It  is 
perhaps  most  readily  understood  by  considering  the  rate  of  change  of 
position  of  a  body  as  discussed  in  mechanics.  If  a  body  is  moving  with 
uniform  velocity,  the  velocity  can  at  once  be  found  by  dividing  the  distance, 

s,  traversed  by  the  time,  t,  taken  to  traverse  it,  hence  velocity  =  -.     The 

velocity  may,  however,  be  continually  altering,  and  it  is  often  desirable  to 
express  the  velocity  at  any  instant.  It  is  not  at  first  sight  evident  how 
this  can  be  done,  as  it  requires  some  time  for  the  particle  to  traverse  any 
measurable  distance,  and  the  velocity  may  be  altering  during  that  time. 
The  nearest  approach  to  the  real  velocity  at  any  instant  will  be  obtained  by 
taking  the  time,  and  therefore  the  distance  traversed,  as  small  as  possible. 
We  might  then  imagine  an  ideal  case  in  which  s  and  t  are  taken  so  small 
that  any  error  due  to  the  variation  of  speed  during  the  time  t  can  be 
neglected.  If  we  represent  these  values  of  5  and  t  by  ds  and  dt  respectively, 
the  speed  of  the  particle  at  any  instant  will  be  given  by  dsjdt. 

In  the  example  given  in  the  text  d(ys)ldt  represents  the  rate  of  change 
of  the  product  with  temperature,  and  the  equation  shows  that  the  rate  of 
change  is  constant. 


DILUTE  SOLUTIONS  127 

where  yl  and  y2  are  the  surface  tensions  of  a  liquid  at  the 
temperatures  ^  and  /2  respectively.  From  equation  (2)  we 
obtain,  for  the  molecular  weight  M, 

•       (3) 


The  surface  tension  of  a  large  number  of  pure  liquids  at 
different  temperatures  has  been  measured  by  Ramsay  and 
Shields  by  observing  the  height  to  which  they  rose  in  capillary 
tubes.  The  results  show  that,  if  M  is  taken  as  the  molecular 
weight  corresponding  with  the  simplest  formula  of  the  liquid, 
the  value  of  c  for  the  majority  of  substances  is  about  -  2-12. 

The  method  may  be  illustrated  l  by  a  determination  of  the 
molecular  weight  of  liquid  carbon  disulphide.  The  experi- 
mental data  are  that  7  =  33-6  (dynes  per  sq.  cm.)  at  19-4°,  and 
29-4  dynes  at  46-1°:  the  specific  volume  (i/density)  of  carbon 
disulphide  at  19-4°  is  1/1-264;  at  46>I°  ^  is  i/i'223-  Hence 


g 


as  compared  with  the  value  76  calculated  from  the  formula. 

As  already  indicated,  the  surface  tension  of  a  liquid  in 
contact  with  its  vapour  diminishes  as  the  temperature  rises  and 
becomes  zero  at  the  critical  temperature,  where  the  surface  of 
separation  beween  liquid  and  vapour  disappears  (p.  50).  If 
temperatures  are  measured  downwards  from  the  critical  tem- 
perature as  zero,  dt  in  equation  (i)  p.  126  has  a  positive  value, 
and  .therefore  c  is  positive.  In  the  next  section  for  convenience 
positive  values  of  the  constant  will  be  used.  It  should  be 
added  that  the  rule  regarding  the  constancy  of  the  expression 
d  (ys)jdt  only  holds  for  temperatures  at  some  distance  (say  50°) 
below  the  critical  temperature. 

Results  of  Measurements  —  Among  the  liquids  which  give 
values  for  c  about  2*12  are  the  following  :  benzine  2*17,  carbon 
tetrachloride  2-11,  silicon  tetrachloride  2*03,  ethyl  iodide  2-10, 
ethyl  ether  2*17,  benzaldehyde  2*16,  aniline  2-05.  On  the  other 

1  Ramsay  and  Shields,  Trans.  Chem.  Soc.,  1893,  63,  1096. 


128        OUTLINES  OK  PHYSICAL  CHEMISTRY 

hand,  many  substances  give  values  for  c  which  are  much  smaller 
than  2- 12  and  which  vary  with  the  temperature.  Thus  for  ethyl 
alcohol  the  values  of  d  [y  (Mz/)2/3]/^/  in  the  neighbourhood  of 
the  temperatures  indicated  are  as  follows  :  i'i8  at  30°,  1-31  at 
90°,  1-46  at  130°,  i'77  at  185°  and  1-94  at  225°.  Among  sub- 
stances which  give  low  values  for  c  are  the  alcohols,  the  organic 
acids  (acetic  acid  0-90  at  16-46°),  acetone  and  water. 

The  most  plausible  explanation  of  these  observations  is  that 
liquids  which  give  constant  values  for  c  approximating  to  2-12 
are  non -associated,  whilst  those  giving  smaller  values  for  this 
factor  are  associated.  We  may  assume  that  association  would 
tend  to  lower  the  molecular  volume  and  thus  give  a  smaller 
value  for  c,  as  is  actually  found.  The  fact  that  for  liquids  with 
abnormally  small  values  for  c  the  latter  increases  steadily  with 
the  temperature  is  also  in  harmony  with  this  explanation,  since 
it  may  be  assumed  that  the  molecular  complexity  diminishes 
with  rise  of  temperature. 

Attempts  have  been  made  to  deduce  from  the  observed 
values  of  d  (ys)jdt  the  degree  of  complexity  of  associated  liquids, 
but  the  results  are  by  no  means  conclusive.  According  to 
Ramsay,  the  association  factor  of  water  at  5°,  25°,  45°  and  85° 
is  3*81,  3*44,  3*13  and  279  respectively;  van  der  Waals,  how- 
ever, deduces  from  the  same  data  considerably  smaller  values 
for  this  factor.1  It  is  quite  certain  that  water  under  ordinary 
conditions  is  a  complex  mixture  of  molecules  of  the  formulae 
H2O,  (H2O)2,  (H2O)3  and  perhaps  still  more  complicated 
aggregates,  but  the  average  degree  of  association  at  any  given 
temperature  is  not  definitely  known. 

Recently  Walden  2  has  shown  that  the  value  of  d  (ys)ldt  for 
palmitic  and  stearic  acids  is  greater  than  5  between  60°  and 
120°.  On  the  basis  of  the  above  interpretation  of  abnormally 
small  values  of  the  temperature  coefficient  in  question,  this 
would  appear  to  indicate  that  the  two  acids  are  highly  dissociated, 
whilst  direct  determinations  in  solution  show  that  the  mole- 
cular weights  are  normal.  This  affords  further  evidence  in 

1  Zeitsch.   Physikal  Chem.,   1894,   13,  713.     See  also  General    Dis- 
cussion, Trans.  Faraday  Soc.,  1910,  6,  71-123. 
*  Zeitsch.  Physikal  Chem.  ign,  75,  555. 


DILUTE  SOLUTIONS  129 

favour  of  the  conclusion  indicated  above,  that  the  rule  of 
Eo'tvos  is  only  approximately  valid. 

The  Nature  of  Surface  Tension — A  deeper  insight  into 
surface  tension  is  obtained  on  the  basis  of  the  molecular  theory. 
We  assume  that  liquid  particles  attract  each  other  with  a  force 
which  falls  off  very  rapidly  with  the  distance.  A  particle  in 
the  interior  of  a  liquid  is  equally  attracted  on  all  sides,  but  a 
particle  in  the  surface  layer  is  attracted  inwards  by  all  the 
particles  of  liquid  within  its  sphere  of  influence,  the  corre- 
sponding attraction  by  the  few  particles  in  the  vapour  space 
being  negligible  in  comparison.  It  follows  that  at  the  surface 
of  liquids  there  is  a  force — tht£  so-called  surface  tension — act- 
ing inwards,  the  liquid  behaving  as  if  it  were  covered  by  an 
elastic  skin. 

It  is  evident  that  work  must  be  done  against  molecular 
attraction  in  bringing  a  particle  to  the  surface  layer,  and  there- 
fore the  formation  of  a  larger  surface  involves  an  expenditure 
of  energy.  The  surface  energy  is  proportional  to  the  product 
of  the  surface  tension  y  and  the  area  of  the  surface,  and  therefore 
the  molecular  surface  energy  is  represented  by  the  expression 
y  (M.v) 2/3,  as  already  mentioned.  A  liquid  tends  to  diminish  the 
area  of  its  surface  as  much  as  possible  in  virtue  of  the  force 
tending  to  draw  the  particles  on  the  surface  towards  the  interior. 
The  tendency  of  liquid  drops  to  assume  a  spherical  shape  and 
of  minute  drops  to  aggregate  to  larger  drops  is  thus  readily 
explained. 

Practical  Illustrations.  Osmotic  Pressure — The  nature 
of  semi-permeable  membranes  may  readily  be  illustrated  by 
Traube's  experiment,  described  on  page  98,  and  also  by 
allowing  drops  of  a  fairly  concentrated  solution  of  potassium 
ferrocyanide  to  fall  into  a  moderately  dilute  solution  of  copper 
sulphate  in  such  a  way  that  the  drops,  which  are  immediately 
surrounded  by  a  film  of  copper  ferrocyanide,  remain  suspended 
at  the  surface  of  the  solution.  It  will  be  observed  that  the 
cells  grow  fairly  rapidly  owing  to  passage  inwards  of  water  from 
the  copper  sulphate  solution,  and,  further,  that  in  consequence 
9 


1 3o       OUTLINES  OF  PHYSICAL  CHEMISTRY 

of  the  increased  concentration  of  the  copper  sulphate  solution 
round  the  drop,  the  concentrated  solution  slowly  flows  down 
through  the  less  concentrated  solution.  The  stream  of  con- 
centrated solution  can  readily  be  recognised  by  the  difference  of 
refractivity,  especially  if  a  bright  light  is  placed  behind  the  vessel 

Selective  Action  of  Semi-permeable  Membrane — This  can  be 
illustrated  by  Nernst's  experiment,  which  is  fully  described  and 
figured  on  page  107. 

A  simple  experiment  illustrating  the  same  principle  has  been 
described  by  Kahlenberg.1  At  the  bottom  of  a  cylindrical  jar 
is  placed  a  layer  of  chloroform,  above  that  a  layer  of  water,  and 
at  the  top  a  layer  of  ether  and  the  jar  is  then  corked.  After 
some  time  it  will  be  noticed  that  the  chloroform  layer  has 
increased  in  depth,  the  water  layer  having  moved  higher  up 
the  tube.  This  phenomenon  depends  on  the  fact  that  ether  is 
much  more  soluble  in  water  than  chloroform.  The  water  there- 
fore acts  like  a  semi-permeable  membrane,  absorbing  the  ether 
and  giving  it  up  to  the  chloroform.  At  the  same  time  the 
chloroform  is  dissolving  in  the  water  and  passing  through  to 
the  ethereal  layer,  but  owing  to  its  much  smaller  solubility,  the 
current  upwards  is  negligible  in  comparison  with  that  downwards. 

In  the  same  paper,  Kahlenberg  describes  a  number  of  experi- 
ments with  rubber  membranes,  which  are  in  many  respects 
instructive. 

Separation  of  Solvent  and  Solute  in  Freezing-point  Experi- 
ments— This  point,  which  is  of  fundamental  importance  for  the 
applicability  of  the  freezing-point  method  of  determining  mole- 
cular weights,  can  be  illustrated  by  partially  freezing  an  aqueous 
solution  of  a  highly  coloured  substance  such  as  potassium 
permanganate  (o'i  per  cent,  solution).  When  the  solution  is 
poured  off,  it  will  be  found  that  the  ice  which  has  separated 
is  practically  colourless. 

The  determination  of  molecular  weights  by  the  boiling-point 
method  (p.  116)  and  by  the  freezing-point  method  (p.  120)  are 
fully  described  in  the  course  of  the  chapter. 

1  jf.  Physical  Cheni.,  1906,  10,  141. 


APPENDIX. 

MATHEMATICAL  DEDUCTION  OF  IMPORTANT 
FORMULAE. 

In  the  course  of  the  present  chapter,  several  formulae  of 
fundamental  importance  have  been  made  use  of,  and  their 
meaning  has  been  fully  illustrated  by  numerical  examples.  For 
the  sake  of  the  more  advanced  student,  simple  deductions  of 
these  formulas  are  given.  It  must  be  understood  that  the 
deductions  are  not  mathematically  strict,  as  certain  of  the 
assumptions  on  which  they  are  based  are  only  approximately 
true. 

The  fundamental  equation  (p.  1 1 2), 

Pi-P*         M      p  M 

~77~    =  jRT  ' 

which  gives  the  connection  between  the  relative  lowering  of 
vapour  pressure  and  the  osmotic  pressure,  and  the  Raoult-van't 
Hoff  formula  (p.  113), 

A  -ft  _  *  ,,-, 

A      ~N    ' 

which  is  readily  derived  from  equation  (i)  by  means  of  the  gas 
laws,  can  be  deduced  by  a  statical-thermodynamical  method 
due  to  Arrhenius  and  also  by  a  cyclical  thermodynamical  method 
due  to  van't  Hoff.  These  deductions  will  now  be  given. 

(i)  The  Statical  Method — A  long  tube  R  containing  a 
solution  of  n  mols  of  a  non-volatile  solute  in  N  mols  of  solvent,1 
is  closed  at  its  lower  end  by  a  semi-permeable  membrane  and 
placed  upright  in  a  vessel  C  which  contains  pure  solvent  (fig. 
20).  The  arrangement  is  covered  by  a  bell-jar  and  all  air  is 
removed  from  the  interior.  When  equilibrium  between  solvent 

1  In  calculating  the  number  of  mols  of  solvent,  its  molecular  weight, 
M,  is  taken  as  that  in  the  form  of  vapour  (p.  112). 

131 


132        OUTLINES  OF  PHYSICAL  CHEMISTRY 


and  solution  is  established  through  the  semi-permeable  mem- 

brane it  is  evident  that  the  osmotic  pressure  is  measured  by 

the  hydrostatic  pressure  of  the 
column  of  liquid  (height  h)  in 
the  tube.  Now  the  pressure 
of  vapour  at  the  level,  a,  of 
the  surface  of  the  solution 
must  be  the  same  inside  and 
outside  the  tube.  If  this  were 
not  the  case,  evaporation  or 
condensation  of  vapour  would 
take  place  at  the  surface,  a, 
and  in  either  case  the  con- 
centration of  the  solution 
would  be  altered  and  the 
equilibrium  between  solution 
and  solvent  disturbed,  which 
is  contrary  to  the  original 
postulate  that  the  system  is  in 
equilibrium.  If  p^  is  the 
vapour  pressure  of  the  solvent 
and  /2  that  of  the  solution, 
the  difference  pl  -  /2  is  the 
difference  of  pressure  at  the 
^13  surface  of  the  solvent  and  at 
FlG  20-  the  level  a.  This  difference 

is  due  to  the  weight  of  a  column  of  vapour  of  height  h  on  unit 

area,  therefore 

Pi-Pi  =  hd      .         .         .          .     (a) 

where  d  is  the  density  of  the  vapour. 

We  have  now  to  express  d  and  h  in  a  different  form.     If  v^ 

is  the  volume  of  i   mol  of  the  vapour,  and  M  the  molecular 

weight  of  the  vapour  in  the  gaseous  form,  we  have  d  =  M/z^. 

When  this  value  of  d  is  substituted  in  the  general  gas  equation, 

plvl  =  RT,  we  obtain 


Further,  as  the  osmotic  pressure,  P,  is  measured  by  the  weight 
of  the  column  h,  therefore  P  =  hs'  where  s'  is  the  density  of 
the  solution.  If  very  dilute  solutions  are  used,  no  appreciable 


APPENDIX  133 

error  will  be  committed  by  substituting  s,  the  density  of  the 
solvent,  for  s',  the  density  of  the  solution.  Substituting  these 
values  of  d  and  h  in  equation  (a)  we  obtain 

P     M/! 

A  -A-J-  RT 

or 

A  -A  _  _M 

A       ~  .RT  '  r' 
which  is  equation  (i),  p.  112. 

From  this  equation,  we  obtain  the  formula, 
A  -A  _  ^ 
A       =N 
as  already  described  (p.  112). 

(2)  The  Cyclical  Method — This  thermodynamical  proof  of 
the  above  formula  depends  upon  the  performance  of  a  cyclic 
process — in  which  the  system  is  finally  brought  back  to  its 
initial  condition — reversibly  at  constant  temperature.  The 
fundamental  point  to  bear  in  mind  in  connection  with  such 
processes  is  that  they  must  be  conducted  throughout  under 
equilibrium  conditions.  It  has  already  been  pointed  out  (p. 
no)  that  the  thermodynamical  proof  of  the  connection  between 
osmotic  pressure  and  the  lowering  of  vapour  pressure  depends 
on  the  work  done  in  removing  solvent  reversibly  from  a  solution. 
There  are  two  principal  methods  by  which  removal  (or  addition) 
of  solvent  can  be  accomplished  : — 

(a)  If  the  solution  is  brought  into  contact  with  its  own 
saturated  vapour  at  constant  temperature,  the  slightest  diminu- 
tion of  the  external  pressure  will  effect  the  removal  of  part  of 
the  solvent ;  on  the  other  hand,  the  slightest  increase  of  the 
external  pressure  will  bring  about  condensation  of  vapour.     If 
the  change  of  volume  of  the  solution  is  in  each  case  very  small 
compared  with  the  total  volume,  the  change  in  concentration 
can  be  neglected. 

(b]  A  solution  is  placed  in  a  cylinder  closed  at  the  bottom 
with  a  semi-permeable  membrane,  the  cylinder  is  immersed  in 
the  pure  solvent,  and  a  movable  piston  rests  on  the  upper 
surface.      The   solution    and   solvent  will   be    in    equilibrium 
through  the  semi -permeable  membrane  when  the  pressure  on 
the  piston  is  equal  to  the  osmotic  pressure.     If  the  pressure  is 
diminished  ever  so  slightly  by  raising  the  piston,  solvent  will 


134       OUTLINES  OF  PHYSICAL  CHEMISTRY 

enter  ;  if  the  pressure  on  the  piston  is  slightly  increased, 
solvent  will  pass  out  through  the  membrane.  We  have,  there- 
fore, a  second  method  by  which  solvent  can  be  separated  from 
a  solution  in  a  reversible  manner,  equilibrium  being  maintained 
throughout.  The  cyclic  process,  in  which  both  these  methods 
are  used,  will  now  be  described. 

(1)  From  a  solution  containing  n  mols  of  solute  to  N  mols 
of  solvent,  a  quantity  of  solvent  which  originally  contained  i 
mol  of  solute  is  squeezed  out  reversibly  by  means  of  the  piston 
and  cylinder  arrangement  ;  the  quantity  thus  removed  is  N/« 
mols.     As  the  original  quantity  of  solution  is  supposed  to  be 
very  great,  its  concentration,  and  therefore  its  osmotic  pressure, 
are  not  appreciably  altered  in  the  process.     As   the  volume 
removed  is  that  which  contained  i  mol  of  solute,  the  work  done 
in  the  process,  which  is  the  product  of  the  volume  and  the 
osmotic  pressure,  is  equal  to 

-RT          ....« 
(p.  2  7)  if  the  gas  laws  apply. 

(2)  The  quantity  of  solvent  is  now  converted  reversibly  into 
vapour  by  expansion  at  the  pressure,  plt  of  the  solvent  ;  the  work 
gained  is  approximately  /1&1  for  i   mol  of  vapour  (the  volume 
of  the  liquid  being  regarded  as  negligible  in  comparison),  or 

~nPi"i  •         •         •     («) 

altogether. 

(3)  The  vapour  is  now  allowed  further  to  expand  till  its 
pressure  falls  to  /2,  the  vapour  pressure  of  the  solution  :  in  this 
process,  an  amount  of  work  is  gained  represented  approximately 
by 


per  mol  of  vapour,  where  (p1  +/2)/2  is  the  mean  pressure 
during  the  small  expansion.  The  quantity  of  vapour  actually 
used  is  N/«  mols,  hence  the  total  work  gained  is 


(4)  The  vapour,  at  the  pressure  /2,  is  now  brought  into 
contact  with  the  solution,  with  which  it  is  in  equilibrium,  and 
condensed  reversibly,  so  that  the  system  regains  its  initial  state. 
The  work  done  on  the  system  in  condensing  the  gas  to  liquid 


APPENDIX  135 

at  the  pressure  /2  is  approximately 

N 
-  -Pfli  .         .  .    (iv) 

As  the  entire  cycle  is  carried  through  at  constant  temperature, 
there  has  on  the  whole  been  no  transformation  of  heat  into  work 
or  -vice  versd  ;  as  the  system  is  finally  brought  back  to  its  initial 
condition,  the  work  expended  must  on  the  whole  be  equal  to 
the  work  gained;  in  other  words  (i)  +  (ii)  4-  (iii)  +  (iv)  must 
be  zero  when  due  regard  is  had  to  the  signs. 

Combining  in  the  first  place  (ii),  (iii),  and  (iv),  we  have 
N  N 


which  reduces  to 


n  \      2      /  n 

where  v  is  the  mean  volume  of  i  mol  of  vapour. 

Substituting  for  v  its  value  from  the  general  gas  equation, 
v  =  RT//,  we  have  finally  l 


n  /j 

as  the  work  gained  in  the  last  three  stages  of  the  cycle.  This 
must  be  equal  to  the  work  done  on  the  system  during  the 
osmotic  removal  of  solvent,  hence 


_  RT  _  0 


or 

as  before. 

The  same  result  may  be  obtained  still  more  simply  by 
integration.  The  work  gained  in  step  (ii)  is  exactly  balanced 
by  that  done  on  the  system  in  (iv),  as  is  evident  from  the 
factors  themselves,  if  the  gas  laws  hold.  In  (iii)  both  the 
pressure  and  the  volume  change  during  the  expansion,  hence 
work  gained  for  i  mol  of  vapour  is  equal  to 

V  o  2>2 

f  pdv  =  f  RT^  =  RT  log,  ^  =  RT  log.^i       (since  p^  =^2) 
-U          V      »  Vl  A 

1  When  the  solution  is  dilute,  p  in  the  denominator  may  be  put  equal 
to  pl  without  sensible  error. 


136      OUTLINES  OF  PHYSICAL  CHEMISTRY 


=  -  RT  log.  =  -  RT  log,    r  - 

P\  V        P\ 

approximately,1  or,  for  the  total  volume  of  vapour, 


The  remainder  of  the  proof  is  as  above. 

Lowering  of  Freezing-point  —  The  above  formula  has 
been  deduced  by  an  isothermal  cyclic  process,  but  the  cyclic 
process  by  which  the  freezing-point  formula  is  deduced  cannot 
be  carried  through  at  constant  temperature.  We  are  therefore 
concerned  with  a  new  question,  that  of  the  relationship  between 
heat  and  work.  The  law  which  applies  in  this  case  is  the 
second  law  of  thermodynamics,  the  deduction  of  which  is  to 
be  found  in  any  advanced  book  on  Physics,  and  which  states 
that  the  maximum  work,  dA,  obtainable  from  a  given  quantity 
of  heat  Q,  in  a  reversible  cycle  is  given  by 


where  the  symbols  have  the  usual  significations  (p.  151). 

A  solution  containing  n  mols  of  solute  in  N  mols  (W  grams) 
of  solvent  is  contained  in  the  cylinder  with  semi  -permeable 
membrane  and  movable  piston  already  described.  The  freezing- 
point  of  the  solvent  is  taken  as  T  and  that  of  the  solution  as 
T  -  dT.  The  stages  in  the  cyclic  process  are  as  follows  :  — 

(1)  At  the  temperature  T  —  dT  an  amount  of  solvent  which 
originally  contained  i  mol  of  solute  is  frozen  out  ;  the  amount 
in  question  is  N/«  mols  or  MN/«  grams.     The  separation  can 
be  carried  out  at  constant  temperature  provided  that  the  amount 
of  solution  is  so  great  that  its  concentration  is  not   thereby 
appreciably  affected.     The  solidified  solvent  is  then  separated 
from  the  solution  and  the  temperature  of  both  raised  to  T. 

(2)  The  solidified  solvent  is  fused,  in  which  process  H  .  — 

calories  are  taken  up,  H  being  the  heat  of  fusion  per  gram. 

(3)  The  fused  solvent  is  then  brought  into  contact  with  the 

1  RT  1  ,  2  is  the  first  term  of  the  expansion  of  the  logarithmic 
function.  Ihe  more  accurate  form  of  the  van't  Hoff-Raoult  formula  is 
l°gf  PilPz  =  >  to  which  the  usual  form  approximates  in  dilute  solution. 


APPENDIX  137 

solution  through  the  semi-permeable  membrane  under  equi- 
librium conditions,  that  is,  when  the  pressure  on  the  piston  is 
equal  to  the  osmotic  pressure  of  the  solution  (p.  133)  and  is 
allowed  to  mix  reversibly  with  the  solution.  The  work  done  in 
this  process  is  represented  by  the  product  of  the  osmotic  pressure, 
P,  and  the  volume,  #,  in  which  i  mol  of  solute  was  dissolved 
and  is,  therefore,  according  to  the  gas  laws,  equal  to  RT. 

(4)  The  system  is  finally  cooled  to  the  original  temperature, 
T  -  ^T,  in  order  to  complete  the  cycle. 

We  have  now  to  consider  the  work  done  in  the  different 
stages  of  the  cycle.  The  heat  expended  in  warming  solution 
and  solvent  in  (i)  is  practically  compensated  l  by  the  heat  given 
out  in  (4).  Further,  an  amount  of  heat  HW/«  is  taken  in  at 
the  higher  temperature  T  and  a  somewhat  less  amount  given 
out  at  T  -  dTT  ;  hence,  by  the  second  law  of  thermodynamics, 
the  work  gained  is 

W     *T 

av^'T- 

The  only  work  done  by  the  system  is  that  expended  in  the 
osmotic  readmission  of  the  solvent,  hence 

W     dl 
RT  =  H.--.-r 

RT2      n 
or  (T£  =  -^-  .  w     .  .     (i) 

If  instead  of  H  we  use  the  molecular  heat  of  fusion,  A,  we 
have  A  =  MH,  and,  further,  N  =  W/M.  Substituting  these 
values  in  equation  (i),  the  latter  reduces  to 


From  this  it  is  evident  that  the  lowering  of  the  freezing-point, 
like  the  relative  lowering  of  vapour  pressure,  is  proportional  to 
the  ratio  of  the  number  of  mols  of  solute  to  the  number  of 
mols  of  solvent. 

From  the  above  formula,  or  more  readily  from  equation  (i), 
above,  an  expression  for  K,  the  depression  produced  when  i  mol 
of  solute  is  dissolved  in  100  grams  of  solvent,  can  readily  be 
obtained.  R  is  approximately  =  2.  when  expressed  in  calories, 

1  The  two  amounts  are  not  exactly  equal,  but  the  difference  can  be 
made  negligible  in  comparison  with  the  heat  taken  up  in  the  second  stage 
of  the  cycle. 


138       OUTLINES  OF  PHYSICAL  CHEMISTRY 

n  —  i  and  W  =  100.  Hence  we  obtain,  for  this  particular 
value  of  dT, 

JT      K       2T2       '         °'°2T2  (*\ 

H    '  ^  =  ~~H~~'      ' 

which  is  the  formula  given  on  p.  120. 

Elevation  of  Boiling-point — By  means  of  a  cyclic  process 
exactly  corresponding  with  that  already  used  in  establishing  the 
freezing-point  formula,  the  formula  connecting  the  elevation  of 
the  boiling-point  with  the  latent  heat  of  vaporisation  of  the 
solvent  is  obtained  in  the  form 

™         0-02T2 

dT  =  -g- 

where  H  is  the  heat  of  vaporisation  of  i  gram  of  solvent  at  the 
temperature  of  the  experiment,  and  T  is  the  boiling-point  of 
the  solvent  on  the  absolute  scale. 

Summary  of  Formulas — (a)  Osmotic  pressure  and  relative 
lowering  of  vapour-pressure.  From  formula  (i)  (p.  112)  we 
obtain  by  substitution 

P  «  j^TflAj:  A  atmospheres  ; 

M  /! 

where  P  is  the  osmotic  pressure,  expressed  in  atmospheres,  s  is 
the  density  of  the  solvent  at  the  absolute  temperature  T,  M  is 
the  molecular  weight  of  the  solvent  in  the  form  of  vapour, 
and  /!  and/2  are  the  vapour-pressures  of  solvent  and  solution 
respectively. 

(b)  Osmotic  pressure  and  lowering  of  freezing-point — From 
formula  (i)  (p.  137),  by  substitution 

loooHj      dT    t 

P  =  .  — -  atmospheres : 

24-22 

where  H  is  the  latent  heat  of  fusion  of  the  solvent  in  calories 
per  gram,  T  is  the  freezing-point  of  the  solvent  on  the  absolute 
scale  and  dT  is  the  freezing-point  depression. 

Osmotic  pressure  and  elevation  of  boiling-point — The  formula, 
which  corresponds  exactly  with  that  for  the  freezing-point 
depression,  is 

loooKr     dT 

P  =    •   ~nrT 

24'22 

where  H  is  the  latent  heat  of  vaporisation  for  i  gram  of  solvent 
at  its  boiling-point,  T  is  the  boiling-point  of  the  solvent  on  the 
absolute  scale,  and  dT  is  the  boiling-point  elevation. 


CHAPTER  VI 
THERMOCHEMISTRY 

General — It  is  a  matter  of  every-day  experience  that 
chemical  changes  are  usually  associated  with  the  develop- 
ment or  absorption  of  heat.  When  substances  enter  into 
chemical  combination  very  readily,  much  heat  is  usually  given 
out  (for  example,  the  combination  of  hydrogen  and  chlorine 
to  form  hydrogen  chloride),  but  when  combination  is  less 
vigorous,  the  heat  given  out  is  usually  much  less,  and,  in 
fact,  heat  may  be  absorbed  in  a  chemical  change.  These 
facts,  which  were  noticed  very  early  in  the  history  of 
chemistry,  led  to  the  suggestion  that  the  amount  of  heat 
given  out  in  a  chemical  change  might  be  regarded  as  a 
measure  of  the  chemical  affinity  of  the  reacting  substances. 
Although,  as  will  be  shown  later,  this  is  not  strictly  true,  there 
is,  in  many  cases,  a  parallelism  between  chemical  affinity  and 
heat  liberation.  In  thermochemistry,  we  are  concerned  with 
the  heat  equivalent  of  chemical  changes. 

Heat  is  a  form  of  energy,  and  therefore  the  laws  regarding 
the  transformations  of  energy  are  of  importance  for  thermo- 
chemistry. It  is  shown  in  text-books  of  physics  that  there 
are  different  forms  of  energy,  such  as  potential  energy,  kinetic 
energy,  electrical  energy,  radiant  energy  and  heat,  and  that 
these  different  forms  of  energy  are  mutually  convertible. 
Further,  when  one  form  of  energy  is  converted  completely 
into  another,  there  is  always  a  definite  relation  between  the 
amount  which  has  disappeared  and  that  which  results.  The 

139 


140        OUTLINES  OF  PHYSICAL  CHEMISTRY 

best-known  example  of  this  is  the  relation  between  kinetic 
energy  and  heat,  which  has  been  very  carefully  investigated  by 
Joule,  Rowland  and  others.  Kinetic  energy  may  be  measured 
in  gram-centimetres  or  in  ergs,  and  heat  energy  in  calories 
(see  p.  xvii).  The  investigators  just  referred  to  found  that 
i  calorie  =  42,650  gram-centimetres  =  41,830,000  ergs,  an 
equation  representing  the  mechanical  equivalent  of  heat. 
From  the  above  considerations  it  follows  that  when  a  certain 
amount  of  one  form  of  energy  disappears  an  equivalent  amount 
of  another  form  of  energy  makes  its  appearance.  These  results 
are  summarised  in  a  law  termed  the  Law  of  the  Conservation  of 
Energy,  which  may  be  expressed  as  follows  :  The  energy  of  an 
isolated  system  is  constant,  i.e.,  it  cannot  be  altered  in  amount 
by  interactions  between  the  parts  of  the  system.  The  proof  of 
this  law  lies  in  the  experimental  impossibility  of  perpetual  motion 
— it  has  been  found  impossible  to  construct  a  machine  which 
will  perform  work  without  the  expenditure  of  energy  of  some 
kind. 

In  dealing  with  chemical  changes,  it  has  been  found  con- 
venient to  employ  the  term  chemical  energy,  and  when  two 
substances  combine  with  liberation  of  heat,  we  say  that  chemical 
energy  has  been  transformed  to  heat.  To  make  this  clear,  we 
will  consider  a  concrete  case,  the  burning  of  carbon  in  oxygen 
with  formation  of  carbon  dioxide,  a  reaction  which,  as  is  well 
known,  is  attended  with  the  liberation  of  a  considerable  amount 
of  heat.  The  reaction  can  be  carried  out  under  such  condi- 
tions that  the  heat  given  out  when  a  definite  weight  of  carbon 
combines  with  oxygen  can  be  measured,  and  it  has  been  found 
that  when  12  grams  of  carbon  and  32  grams  of  oxygen  unite, 
94,300  calories  are  liberated.  This  result  may  conveniently  be 
represented  by  the  equation 

C  +  O2  =  CO2  +  94,300  cal. 

in  which  the  symbols  represent  the  atomic  weights  of  the 
reacting  elements  in  grams.  The  above  equation  is  an  illus- 
tration of  the  conversion  of  chemical  energy  into  heat — 12 


THERMOCHEMISTRY  141 

grams  of  free  carbon  and  32  grams  of  free  oxygen  possess 
94,300  cal.  more  energy  than  the  44  grams  of  carbon  dioxide 
formed  by  their  union.  From  these  and  similar  considerations 
it  follows  that  the  free  elements  must  have  much  intrinsic 
energy,  but  the  absolute  amount  of  this  energy  in  any  par- 
ticular case  is  quite  unknown.  Fortunately,  this  is  a  matter 
of  secondary  importance,  as  chemical  changes  do  not  depend 
on  the  absolute  amounts  of  energy,  but  only  on  the  differences 
of  energy  of  the  reacting  systems. 

So  far,  we  have  implicitly  assumed  that  the  increase  or  de- 
crease of  internal  energy  when  a  system  A  changes  to  a  system 
B  is  measured  by  the  heat  absorbed  or  given  out  during  the 
reactions  ;  but  this  is  not  necessarily  the  case.  In  particular, 
external  work  may  be  done  during  the  change,  by  which  part  of 
the  energy  is  used  up,  or  heat  may  be  produced  at  the  expense 
of  external  work  (cf.  p.  27).  If  the  total  diminution  of  internal 
energy  in  the  change  A  ->  B  is  represented  by  U,  the  heat  given 
out  by  —  Q,  and  the  external  work  done  by  the  reacting  sub- 
stances during  the  transformation  by  A,  we  have,  by  the  prin- 
ciple of  the  conservation  of  energy, 

U  =  A  -  Q. 

The  factor  A  is  only  of  importance  when  gases  are  involved  in 
the  chemical  change  ;  the  method  of  calculating  the  work  done 
in  changes  of  volume  of  gases  has  already  been  given  (p.  27). 

Hess's  Law — It  is  an  experimental  fact  that  when  the  same 
chemical  change  takes  place  between  definite  amounts  of  two 
substances  under  the  same  conditions  the  same  amount  of  heat 
is  always  given  out  provided  that  the  final  product  or  products 
are  the  same  in  each  case.  Thus  when  12  grams  of  carbon 
combine  with  32  grams  of  oxygen  with  formation  of  carbon 
dioxide,  94,300  cal.  are  always  liberated,  quite  independently  of 
the  rate  of  combustion  or  of  the  nature  of  the  intermediate  pro- 
ducts. This  law  was  first  established  experimentally  by  Hess  in 
1840,  and  may  be  illustrated  by  the  conversion,  by  two  different 
methods,  of  a  system  consisting  of  i  mol  of  ammonia  and  of 


142       OUTLINES  OF  PHYSICAL  CHEMISTRY 

hydrochloric  acid  respectively  and  a  large  amount  of  water,  each 
taken  separately,  into  a  system  consisting  of  i  mol  of  ammonium 
chloride  in  a  large  excess  of  water.  By  the  first  method  we 
measure  (a)  the  heat  change  when  i  mol  of  gaseous  ammonia 
and  i  mol  of  gaseous  HC1  combine,  (b)  the  heat  change  when 
the  solid  ammonium  chloride  is  dissolved  in  a  large  excess  of 
water ;  by  the  second  method  we  measure  the  heat  changes 
when  (c)  i  mol  of  ammonia,  (d)  i  mol  of  hydrochloric  acid  are 
dissolved  separately  in  excess  of  water,  and  (e)  when  the  two 
solutions  are  mixed.  The  results  obtained  were  as  follows  : — 

First  Way. 

(a]  NH3  gas  +  HC1  gas  =  +42,100  cal. 

(b)  NH4C1  +  aq  =  -    3,900  cal. 


38,200  cal. 
Second  Way. 

(c)  NH3gas  +  aq  =  +   8,400  cal. 

(d}  HC1  gas  +  aq  =  +  1 7,300  cal. 

(e)  HClaq  +  NH3tiq        =  +  12,300  cal. 


38,000  cal. 

As  will  be  seen,  a+d=c+d+e  within  the  limits  of  ex- 
perimental error. 

It  can  easily  be  shown  that  Hess's  law  follows  at  once  from 
the  principle  of  conservation  of  energy. 

This  law  is  of  the  greatest  importance  for  the  indirect  deter- 
mination of  the  heat  changes  involved  in  certain  reactions 
which  cannot  be  carried  out  directly.  For  example,  we  cannot 
determine  directly  the  heat  given  out  when  carbon  combines 
with  oxygen  to  form  carbon  monoxide.  The  heat  given  out 
when  12  grams  of  carbon  burn  to  carbon  dioxide  is  94,300 
cal.,  which  is,  by  Hess's  law,  equal  to  that  produced  when  the 
same  amount  of  carbon  is  burned  to  monoxide  and  the  latter 
then  converted  to  dioxide.  The  latter  change  gives  out  68,100 


THERMOCHEMISTRY  143 

cal.,  and  the  reaction  C  +  O  =  CO  must  therefore  be  associated 
with  the  liberation  of  94,300  -  68,100  =  26,200  cal. 

Representation  of  Thermochemical  Measurements. 
Heat  of  Formation — As  has  already  been  pointed  out,  the 
results  of  thermochemical  measurements  may  be  conveniently 
represented  by  making  the  ordinary  chemical  equation  into  an 
energy  equation,  for  example, 

C  +  O2  =  CO2  +  94,300  cal. 

94,300  cal.  is  termed  the  heat  of  formation  of  carbon  dioxide 
from  its  elements.  This  equation  is,  however,  not  complete, 
inasmuch  as  we  do  not  know  the  intrinsic  energy  associated 
with  free  carbon  and  oxygen  respectively,  nor  do  we  know  the 
differences  of  energy  between  the  various  elements,  as  they  are 
not  mutually  convertible  by  any  known  means.  We  may  there- 
fore choose  any  arbitrary  value  for  the  intrinsic  energies  of  the 
elements,  and  it  has  been  found  most  convenient  to  put  them 
all  equal  to  zero.  On  this  basis  the  complete  energy  equation 
for  the  formation  of  carbon  dioxide  can  be  written 
0  +  0  =  CO2  +  94,300  cal., 
whence  CO2  =  —  94,300  cal., 

that  is,  the  energy  of  i  mol  of  carbon  dioxide  is  —94,300 
calories.  Therefore,  in  writing  an  energy  equation,  the  formula 
of  a  compound  is  replaced  by  the  heat  of  formation  with  its  sign 
reversed,  which  represents  its  intrinsic  energy. 

We  can  make  use  of  this  simple  rule  in  two  ways  :  (i)  to 
calculate  the  heat  set  free  in  a  chemical  change  when  the  heats 
of  formation  of  the  reacting  substances  are  known;  (2)  to 
calculate  an  unknown  heat  of  formation  when  all  the  other  heats 
of  formation  and  the  heat  given  out  in  the  chemical  change 
are  known. 

As  an  example  of  the  first  application,  we  may  calculate  the 
heat  change,  x,  when  copper  is  displaced  from  copper  sulphate 
in  dilute  solution  by  metallic  zinc  according  to  the  equation 

CuSO4  aq  +  Zn  =  ZnSO4  aq  +  Cu. 


144        OUTLINES  OF  PHYSICAL  CHEMISTRY 

The  heat  of  formation  (from  its  elements)  of  copper  sulphate  in 
dilute  solution  is  198,400  cal.  and  of  zinc  sulphate  under  the 
same  conditions  248,500  cal.  The  energy  equation  for  the 
chemical  change  is  therefore 

Zn  +  CuSO4  aq  =  Cu  +  ZnSO4  aq 

o  +  (-198,400)  =  o  +  (-248,500)  +  x  cal., 

the  intrinsic  energies  of  the  elements  and  compounds  being 
written  below  the  respective  formulae.  As  248,500  cal.  are 
given  out  in  the  formation  of  zinc  sulphate  and  198,400  cal. 
absorbed  when  copper  sulphate  yields  metallic  copper,  x,  the 
total  heat  liberated  in  the  reaction  is  248,500  -  198,400  = 
50,100  cal. 

As  an  example  of  the  second  application,  the  heat  of  forma- 
tion of  methane  from  its  elements,  which  cannot  be  determined 
directly,  will  be  calculated.  The  heat  given  out  when  i  mol 
of  this  compound  is  burned  completely  in  oxygen  is  213,800 
cal.,  and  the  heat  of  formation  of  the  products,  carbon  dioxide 
and  liquid  water,  are  94,300  and  68,300  cal.  respectively.  Re- 
presenting the  heat  of  formation  of  methane  by  x,  its  intrinsic 
energy  therefore  by  -  x,  we  have  the  equation 

CH4  +  2O2  =  CO2  +  2H2O 

-x  +  o  =  -94,300  +  (-2  x  68,300)  +  213,800  cal. 

Whence  x  —  17,100  cal. 

A  compound  such  as  methane,  which  is  formed  with  libera- 
tion of  heat,  is  termed  an  exothermic  compound,  whilst  one 
which  is  formed  with  absorption  of  heat  is  termed  an  endo- 
thermic  compound. 

The  majority  of  stable  compounds  are  exothermic.  Among 
the  best-known  endothermic  compounds  are  carbon  disulphide, 
hydriodic  acid,  acetylene,  cyanogen  and  ozone.  It  is  not 
always  easy  to  determine  directly  whether  a  compound  is 
exothermic  or  endothermic,  but  this  may  be  done  indirectly 
by  carrying  out  a  chemical  change  with  the  compound  itself 
and  with  the  components  separately  and  comparing  the  heat 


THERMOCHEMISTRY  145 

changes  in  the  two  cases.  The  method  may  be  illustrated  by 
reference  to  carbon  disulphide.  When  burnt  completely  in 
oxygen,  the  gaseous  compound  gives  out  265,100  cal.  accord- 
ing to  the  equation 

CS2  +  3O2  =  CO2  +  2SO2  +  265,100  cal. 

Hence,  representing  the  intrinsic  energy  of  the  compound  by 
-  x,  we  have,  for  the  energy  equation, 

-  x  +  o  =  +  ( -  94,300)  +  (  -  2  x  71,000)  +  265,100,  . 
and  —  x  =  +  28,800  cal.     The  intrinsic  energy  of  carbon  disul- 
phide is  therefore  28,800  cal. ;   that  is,  the  compound  has  28,800 
cal.  more  energy  than  the  elements  from  which  it  is  formed. 

Heat  of  Combustion — Whilst  a  great  many  inorganic  re- 
actions are  suitable  for  thermochemical  measurements,  this  is 
not  in  general  the  case  for  organic  reactions ;  in  fact,  the  only 
reaction  which  is  largely  used  for  the  purpose  is  combustion  in 
oxygen  to  carbon  dioxide  and  water.  The  heat  given  out  in 
such  a  reaction  is  termed  the  heat  of  combustion^  and  from  this, 
by  application  of  Hess's  law,  the  heats  of  formation  can  be  cal- 
culated, as  has  been  done  for  methane  and  carbon  disulphide, 
in  the  preceding  section.  Further,  the  heat  given  out  in  a 
chemical  change  can  readily  be  calculated  by  Hess's  law  when 
the  heats  of  combustion  of  the  reacting  substances  are  known — 
it  will  clearly  be  equal  to  the  sum  of  the  heats  of  combustion 
of  the  substances  which  disappear  less  the  sum  of  the  heats  of 
combustion  of  the  substances  formed.  As  an  example,  the  heat 
of  formation  of  ethyl  acetate  from  ethyl  alcohol  and  acetic  acid 
may  be  calculated.  The  heat  of  combustion  of  ethyl  alcohol  is 
34,000  cal.,  of  acetic  acid  21,000  cal.,  and  of  ethyl  acetate  55,400 
cal.,  whence  the  heat  of  formation  of  ethyl  acetate  is  34,000  + 
21,000  -  55,400  =  -  400  cal. 

Thermochemical  Methods— Two  principal  methods  are 
employed  in  measuring  the  heat  changes  associated  with 
chemical  reactions.  If  the  reaction  takes  place  in  solution,  the 
water  calorimeter,  so  largely  used  for  purely  physical  measure- 
ments, may  be  employed.  For  the  determination  of  heats  of 
10 


i4f>        OUTLINES  OF  PHYSICAL  CHEMISTRY 

combustion,  on  the  other  hand,  in  which  solids  or  liquids  are 
burned  completely  in  oxygen,  special  apparatus  has  been  de- 
signed by  Thomsen,  Berthelot,  Favre  and  Silbermann  and  others. 

(a)  Reactions  in  Solution — The  change  (chemical  reaction, 
dilution  or  dissolution),  the  thermal  effect  of  which  is  to  be 
measured,  is  brought  about  in  a  test-tube  deeply  immersed  in 
a  large  quantity  of  water,  and  the  rise  of  temperature  of  the 
water  is  measured  with  a  sensitive  thermometer.  When  the 
weight  of  the  water  and  the  heat  capacity  of  the  calorimeter 
are  known,  the  heat  given  out  in  the  reaction  can  readily  be 
calculated.  Allowance  must,  of  course,  be  made  for  the  heat 
capacity  of  the  solution  in  the  test-tube. 

A  simple  modification  of  Berthelot's  calorimeter,  used  by 
Nernst,  is  shown  in  Fig.  21.  It  consists  of  two  glass  beakers, 
the  inner  one  being  supported  on  corks,  as  shown,  and  nearly 
filled  with  water.  Through  the  wooden  cover,  X,  of  the  outer 
beaker  pass  a  thin-walled  test-tube,  A,  in  which  the  reaction 
takes  place,  an  accurate  thermometer  B,  and  a  stirrer  C  of 
brass,  or,  better,  of  platinum.  The  water  in  the  calorimeter 
is  stirred  during  the  reaction,  which  must  be  rapid,  and  the 
heat  of  reaction  can  then  be  calculated  in  the  usual  way 
when  the  weight  of  water  in  the  calorimeter  and  the  rise  of 
temperature  are  known.  Experiments  on  neutralization  and 
on  heat  of  solution  are  conveniently  made  in  the  inner  beaker, 
the  solution  itself  serving  as  calorimetric  liquid.  For  dilute 
aqueous  solutions,  it  is  sufficiently  accurate  to  assume  that  the 
heat  capacity  of  the  solution  is  the  same  as  that  of  water. 

The  chief  source  of  error  in  the  measurements  is  the  loss 
of  heat  by  radiation,  which  is  minimised  (a)  by  choosing  for 
investigation  reactions  which  are  complete  in  a  comparatively 
short  time ;  (b]  by  making  the  heat  capacity  of  the  calorimeter 
system  large.  It  is  of  advantage  so  to  arrange  matters  that 
the  temperature  of  the  calorimeter  liquid  is  1-2°  below  the 
atmospheric  temperature  before  the  reaction,  and  1-2°  above 
it  after  the  reaction. 


THERMOCHEMISTRY 


147 


(£)  Combustion  in  Oxygen — This  may  conveniently  be  carried 
out  in  Berthelot's  calorimetric  bomb,  a  vessel  of  steel,  lined 
with  platinum  and  provided  with  an  air-tight  lid.  The  sub- 
stance for  combustion  is  placed  in  the  bomb,  which  is  filled 
with  oxygen  at  20-25  atmo- 
spheres' pressure.  The  whole 
apparatus  is  then  sunk  in  the 
water  of  the  calorimeter,  and 
the  combustion  initiated  by 
heating  electrically  a  small 
piece  of  iron  wire  placed  in 
contact  with  the  solid. 

Results  of  Thermochemi- 
cal  Measurements  —  Some 
of  the  more  important  results 
of  thermochemical  measure- 
ments have  already  been  inci- 
dentally referred  to  in  the 
preceding  paragraphs.  In 
stating  the  results  of  thermo- 
chemical measurements,  the 
condition  of  the  substances 
taking  part  in  the  reaction  must 
always  be  clearly  stated.  This 
applies  not  only  to  the  physical 
state,  in  connection  with  which 
allowance  must  be  made  for 
heat  of  vaporization,  heat  of 
fusion,  etc.,  but  also  to  the 
different  allotropic  modifications  of  the  solid.  Thus  mono- 
clinic  sulphur  has  2300  cal.  more  internal  energy  than  rhombic 
sulphur,  and  yellow  phosphorus  27,300  cal.  more  than  the  red 
modification. 

The  correction  for  change  of  state  is  often  very  great.     For 
the  transformation  of  water  to  steam  at   100°,  it  amounts  to 


FIG.  21. 


148       OUTLINES  OF  PHYSICAL  CHEMISTRY 

about  537  x  18  =  9566  calories  per  mol.  If,  instead  of  the 
heat  of  formation  of  liquid  water,  which  is  68,300  cal.,  the 
heat  of  formation  of  water  vapour  is  required,  it  is  68,300  — 
9570  =  58,730  cal.  in  round  numbers.1 

As  regards  the  thermochemistry  of  salt  solutions,  one  or  two 
experimental  results  may  be  mentioned  which  will  find  an 
interpi  etation  later.  When  dilute  solutions  of  two  salts,  such 
as  potassium  nitrate  and  sodium  chloride,  are  mixed,  heat  is 
neither  given  out  nor  absorbed.  This  important  result  is 
termed  the  Law  of  thermoneutrality  of  salt  solutions  (p.  279). 
Further,  when  a  mol  of  any  strong  monobasic  acid  is  neutralized 
by  a  strong  base,  the  same  amount  of  heat,  13,700  cal.,  is 
always  liberated  (p.  284). 

The  heat  of  formation  of  salts  in  dilute  aqueous  solution  is 
obtained  by  the  addition  of  two  factors,  one  pertaining  to  the 
positive,  the  other  to  the  negative  part  of  the  molecule ;  in 
other  words,  the  heat  of  formation  of  salts  in  dilute  solution 
is  a  distinctly  additive  property.  The  same  is  true  to  some 
axtent  for  the  heat  of  combustion  of  organic  compounds.  For 
example,  the  difference  in  the  heat  of  combustion  of  methane 
and  ethane  is  158,500  cal.,  and  in  general,  for  every  increase 
of  CH2,  the  heat  of  combustion  increases  by  about  158,000  cal. 
From  these  and  similar  results,  we  can  deduce  the  general  rule 
that  equal  differences  in  composition  correspond  to  approxi- 
mately equal  differences  in  the  heat  of  combustion.  We  may  go 
further,  and  obtain  definite  values  for  the  heat  of  combustion 
of  a  carbon  atom  and  a  hydrogen  atom  as  has  already  been 
done  for  atomic  volumes ;  the  molecular  heat  of  combustion 
is  then  the  sum  of  the  heats  of  combustion  of  the  individual 
atoms.  Experience  shows  that  when  allowance  is  made  for 
double  and  triple  bindings,  the  observed  and  calculated  values 
for  the  heats  of  combustion  of  hydrocarbons  agree  fairly  well. 

Relation  of  Chemical  Affinity  to  Heat  of  Reaction- 
Very  early  in  the  study  of  chemistry,  it  becomes  evident  that 
chemical  actions  may  be  divided  into  two  classes  :  (i)  those 

1  The  connection  to  be  applied  for  changes  in  the  volume  of  gases  has 
already  been  discussed  (p.  27) :  it  amounts  to  2  T  cal.  per  mol. 


THERMOCHEMISTRY  149 

which  under  the  conditions  of  the  experiment  are  spontaneous 
or  proceed  of  themselves,  once  they  are  started,  e.g.,  the  com- 
bination of  carbon  and  oxygen ;  (2)  those  which  only  proceed 
when  forced  by  some  external  agency,  e.g.,  the  splitting  up  of 
mercuric  oxide  into  mercury  and  oxygen.  In  this  section  we 
are  concerned  only  with  spontaneous  changes. 

The  direction  in  which  a  chemical  change  takes  place  in  a 
system  depends  on  the  energy  relations  of  the  system.  We 
are  accustomed  to  say  that  the  direction  of  the  change  is 
determined  by  the  chemical  affinity  of  the  reacting  substances, 
and  it  is  a  matter  of  the  utmost  importance  to  obtain  a 
numerical  expression  for  the  chemical  affinity  or  driving  force 
in  a  chemical  system,  the  driving  force  being  defined  in  such 
a  way  that  the  chemical  change  proceeds  in  the  direction  in 
which  it  acts,  and  comes  to  a  standstill  when  the  driving  force 
is  zero. 

Most  reactions  in  which  there  is  a  considerable  transformation 
of  chemical  energy,  and  therefore  a  considerable  development 
of  other  forms  of  energy,  such  as  heat  or  electrical  energy, 
proceed  very  rapidly  (for  example,  the  combination  of  hydrogen 
and  chlorine),  whilst  reactions  in  which  less  chemical  energy  is 
transformed  are  usually  much  less  vigorous  (for  example,  the 
combination  of  hydrogen  and  iodine).  It  seems,  therefore,  at 
first  sight  plausible  to  measure  the  chemical  affinity  in  a  system 
by  the  amount  of  heat  liberated  in  the  reaction  (Thomsen, 
Berthelot).  As,  however,  chemical  affinity  has  been  defined  as 
acting  in  the  direction  in  which  spontaneous  chemical  change 
takes  place,  it  would  follow  that  only  reactions  in  which  heat 
is  given  out  can  take  place  spontaneously.  This  deduction  is 
contrary  to  experience.  Water  can  spontaneously  pass  into 
vapour,  although  in  the  process  heat  is  absorbed,  and  many 
salts,  such  as  ammonium  chloride,  dissolve  in  water  with 
absorption  of  heat.  It  is  clear,  therefore,  that  chemical  affinity, 
as  above  defined,  cannot  be  measured  by  the  total  heat  liberated 
in  the  reaction. 


i5c        OUTLINES  OF  PHYSICAL  CHEMISTRY 

The  importance  for  technical  purposes  of  such  a  reaction  as 
the  burning  of  coal  in  oxygen  is  not  so  much  the  total  heat 
obtainable  by  the  change  as  the  amount  of  work  which  the 
change  may  be  made  to  perform.  In  a  similar  way,  /'/  has  been 
found  convenient  to  measure  the  chemical  affinity  of  a  system  by 
the  maximum  amount  of  external  work  which,  under  suitable 
conditions^  the  reaction  may  be  made  to  perform.  This  is  a 
special  case  of  a  very  comprehensive  natural  law,  which  may 
be  expressed  as  follows :  All  spontaneous  reactions  (in  the 
widest  sense,  including  neutralization  of  electrical  charges, 
falling  of  liquids  to  a  lower  level,  etc.)  can  be  made  to 
perform  work,  and  all  reactions  which  can  be  made  to  per- 
form work  are  spontaneous,  i.e.,  can  proceed  of  themselves 
without  the  application  of  external  forces.  The  available 
energy  of  a  chemical  reaction,  that  is,  that  part  of  the  total 
energy  which  at  constant  temperature  and  under  suitable  condi- 
tions can  be  made  to  perform  an  equivalent  of  work,  has  been 
termed  "  free  energy  "  by  Helmholtz.  The  chemical  affinity 
or  driving  force  of  a  reaction  is  not  proportional  to  the  total 
change  of  energy,  but  to  the  change  in  the  available  or  free  energy. 

The  total  energy,  U,  of  a  chemical  change  can  be  obtained 
in  the  form  of  heat  by  carrying  out  the  reaction  under  such 
conditions  that  no  external  work  is  done  (p.  141).  We  have 
now  to  consider  what  is  the  connection  between  the  total 
decrease  of  energy,  U,  and  the  decrease  of  available  or  free 
energy,  which  may  be  termed  A.  This  question  is  closely 
connected  with  the  conditions  under  which  heat  can  be  con- 
tinuously transformed  into  work.  We  have  to  find  an  expres- 
sion for  the  maximum  work  performed  in  a  cycle  in  which  the 
heat  is  taken  in  at  the  temperature  T,  and  given  out  at  the 
slightly  lower  temperature  T  -  dT.  The  principle  to  be  used  for 
this  purpose  is  that  employed  in  the  theory  of  the  steam-engine, 
but  it  has  universal  applicability.  According  to  this,  the  maxi- 
mum work,  dA.,  obtainable  from  a  given  quantity  of  heat  Q  is 
given  by 


THERMOCHEMISTRY  151 

^A  =  QJ^     .  (i) 

Equation  (i)  is  the  mathematical  expression  of  the  second  law 
of  thermodynamics. 

We  have  already  seen  (p.  141)  that  the  law  of  the  conservation 
of  energy,  sometimes  termed  the  first  law  of  thermodynamics, 
may  be  expressed  in  the  form 

U  =  A-Q    .         .         .         .       (2) 

in  which  A  represents  the  external  work  done  when  the  total 
diminution  of  energy  is  U  and  the  heat  given  out  is  -  Q.  Now 
dA,  in  equation  (i),  is  the  difference  of  the  maximum  amounts 
of  work  obtainable  in  isothermal  processes  at  the  temperatures 
T  and  T-dT;  thus  A  has  the  same  significance  here  as  in 
equation  (2).  We  may  therefore  obtain  an  expression  in  which 
Q  does  not  occur  by  substituting  for  Q  in  equation  (i)  its  value 
A  -  U,  from  equation  (2).  We  thus  obtain 

A-U  =  T^         .        .        .      (3) 

in  which  U  represents  the  total  change  of  energy  in  the  re- 
action, A  represents  the  free  energy  or  chemical  affinity,  and 
dA/dT  the  rate  of  change  of  the  free  energy  with  tempera- 
ture. Equation  (3)  is  the  fundamental  equation  for  isothermal 
chemical  changes,  that  is,  for  chemical  changes  which  take 
place  at  constant  temperature.  The  equation  shows  that  the 
change  in  the  free  energy  differs  from  the  change  in  the  total 
energy  by  an  amount  T(dA/dT),  and  that  the  two  quantities 
can  only  be  identical  when  the  right-hand  side  of  the  equation 
is  zero. 

As  the  above  equation  has  been  derived  from  the  second 
law  of  thermodynamics,  it  follows  that  the  free  energy  can  be 
determined  only  for  reactions  which  can  be  made  completely 
reversible.  By  complete  reversibility  we  mean  that  if  a  system, 
in  changing  from  the  state  A  -to  B,  performs  an  amount  of 


152        OUTLINES  OF  PHYSICAL  CHEMISTRY 

work,  X,  it  can  be  restored  to  the  condition  A  by  the  expendi- 
ture of  the  same  amount  of  work.  Reactions  such  as  the  dis- 
sociation of  calcium  carbonate  in  a  closed  space  by  heat  are 
reversible  (p.  173),  but  a  reaction  in  which  gases  escape  from 
the  system,  as  when  zinc  is  dissolved  in  acid,  are,  of  course, 
not  reversible.  Many  reactions  which  are  not  reversible  under 
ordinary  conditions  can  be  carried  out  reversibly  in  galvanic 
elements  (for  example,  the  displacement  of  copper  from  solu- 
tion by  zinc  in  the  Daniell  element),  and  therefore  measure- 
ments of  electromotive  force  are  largely  used  for  determinations 
of  the  free  energy  in  a  system.  As  will  be  shown  later  (p.  332), 
when  a  chemical  reaction  takes  place  reversibly  in  a  galvanic 
cell,  the  electromotive  force  of  the  cell  is  proportional  to  the 
free  energy  of  the  reaction. 

It  is  beyond  the  scope  of  this  book  to  discuss  fully  the 
many  deductions  which  may  be  made  from  equation  (3),  and 
only  one  important  consequence  will  be  mentioned.  At  the 
absolute  zero  (T  =  o)  the  right-hand  side  of  the  equation 
becomes  zero,  and  therefore  the  total  change  of  energy  U 
(which  is  equal  to  the  heat  of  reaction  Q  when  no  external 
work  is  done)  is  equal  to  the  change  in  the  free  energy  A.  In 
other  words,  at  the  absolute  zero,  all  reactions  would  proceed 
in  the  direction  in  which  heat  is  given  out,  and  the  heat  evolved 
would  then  be  a  measure  of  the  chemical  affinity.  As  the 
absolute  zero  is  at  present  unattainable,  this  statement  by  itself 
is  of  no  practical  importance,  but  the  form  of  equation  (3) 
indicates  that  at  temperatures  not  very  far  from  the  absolute 
zero,  U  and  A  may  often  not  be  greatly  different.  As  ordinary 
temperatures  are  relatively  not  very  far  from  the  absolute  zero, 
we  can  now  understand,  from  the  approximation  in  the  values 
of  U  and  A,  why  so  many  chemical  reactions  proceed  of  them- 
selves in  the  direction  in  which  heat  is  given  out  (cf.  p.  149). 

Although  the  dissolving  of  some  salts  in  water  is  attended 
with  absorption  of  heat,  it  can  be  shown  that  the  free  energy  has 
diminished,  and  the  same  is  true  of  the  vaporization  of  water, 


THERMOCHEMISTRY  153 

In  these  extreme  cases,  not  only  are  A  and  U  of  very  different 
numerical  value,  but  they  even  have  opposite  signs. 

Practical  Illustrations — As  already  mentioned,  the  heat 
evolved  in  certain  chemical  reactions  can  conveniently  be 
measured  by  causing  the  reaction  to  proceed  in  the  glass  tube, 
A,  Fig.  21,  and  obtaining  the  heat  of  the  reaction  from  the  rise 
in  temperature  of  the  water.  This  form  of  apparatus  is,  how- 
ever, more  useful  for  measuring  heats  of  dilution  and  of  solution. 
If,  for  example,  we  wish  to  determine  the  heat  of  solution  of 
potassium  chloride,  a  known  weight  of  water  is  placed  in  the 
inner  beaker,  a  known  weight  of  salt  in  the  tube,  A,  and  when 
the  salt  may  be  expected  to  be  at  the  same  temperature  as 
the  water,  the  glass  tube  is  broken  with  a  glass  rod,  the  salt 
dissolved  in  the  water  by  stirring,  and  the  change  of  temperature 
read  off  on  the  thermometer. 

For  reactions  in  dilute  solution,  the  tube  A  may  be  dispensed 
with,  and  the  outer  beaker  supported  on  corks  in  a  third  beaker^ 
so  as  to  minimise  the  loss  of  heat  by  radiation.  In  this  apparatus 
the  heat  of  neutralization  of  a  dilute  acid  (half  normal  hydro- 
chloric acid)  by  an  equal  volume  of  dilute  alkali  (sodium 
hydroxide)  may  be  determined.  J  litre  of  the  hydrochloric 
acid  is  placed  in  the  inner  beaker,  at  a  temperature  2°  to  3° 
below  that  of  the  atmosphere,  J  litre  of  N/2  sodium  hydroxide, 
of  known  temperature,  is  rapidly  poured  into  the  acid  with 
constant  stirring.  The  highest  temperature  attained  is  noted* 
If  the  solutions  are  at  the  same  temperature  before  mixing,  the 
rise  of  temperature  will  be  about  3*4°,  corresponding  with  the 
fact  that  the  heat  of  neutralization  of  i  mol  of  sodium  hydroxide 
by  hydrochloric  acid  is  13,700  cal.  (p.  148).  Measurements  of 
heat  of  neutralization,  heat  of  dilution,  etc.,  may  be  made  still 
more  conveniently  with  metal  calorimeters,  as  used  in  physical 
laboratories ;  the  vessels  should  be  well  polished  so  as  to 
minimise  the  loss  of  heat  by  radiation. 

Measurements  should  also  be  made  with  some  form  of  com- 
bustion calorimeter,  if  available. 


CHAPTER   VII 

EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS.     LAW 
OF  MASS  ACTION 

General — In  the  last  chapter  we  have  been  mainly  concerned 
with  the  heat  equivalents  of  chemical  charges.  We  have  now 
to  deal  with  chemical  transformations,  with  reference  more 
particularly  to  the  dependence  of  the  rate  and  extent  of  chemical 
reactions  on  the  conditions. 

When  a  chemical  reaction  can  take  place  between  two  sub- 
stances, it  is  usual  to  say  that  they  have  a  certain  "  chemical 
affinity  "  for  each  other.  From  very  early  times  the  question  as 
to  the  nature  of  this  affinity  has  been  discussed,  but  up  to  the 
present  with  very  little  success.  Newton  was  of  opinion  that  the 
small  particles  of  different  kinds  attract  each  other  much  as  the 
heavenly  bodies  do  (gravitational  attraction),  and  that  the  attrac- 
tion falls  off  very  rapidly  with  the  distance.  According  to  this 
view,  if  we  have  three  substances,  A,  B  and  C,  and  the  attraction 
between  A  and  B  is  greater  than  that  between  A  and  C,  then  B 
will  completely  displace  C  from  its  combination  with  A ;  in 
other  words,  the  reaction  AC  +  B  ->  AB  +  C  will  be  complete 
in  the  direction  indicated  by  the  arrow.  These  views  found 
their  expression  in  the  so-called  affinity  tables  drawn  up  by 
Stahl,  Bergmann  and  others,  in  which  the  elements  were  arranged 
in  the  order  in  which  they  could  displace  each  other  from  com- 
bination. Somewhat  later,  Berzelius  developed  his  electro- 
chemical theory,  according  to  which  the  attractions  concerned 
in  chemical  changes  are  electrical  in  character,  but  this  theory 


EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS     155 

proved  in  many  respects  unsatisfactory.  The  importance  of  the 
conditions,  more  particularly  as  regards  the  relative  amounts  of 
the  reacting  substances  and  the  temperature,  on  the  direction 
and  amount  of  chemical  change,  only  came  to  be  recognised 
very  gradually. 

In  recent  years,  the  question  as  to  why  certain  chemical 
changes  take  place  has  been  relegated  to  the  background  and 
attention  has  been  directed  to  how  they  take  place.  As  mentioned 
in  the  last  chapter,  it  has  been  found  possible  in  many  cases 
to  obtain  numerical  values  for  the  chemical  affinity,  without 
troubling  about  its  exact  nature.  When  for  any  reaction  the 
chemical  affinities  of  the  reacting  substances  are  known,  as  well 
as  the  dependence  of  the  reaction  on  the  conditions,  the  reaction 
is  completely  described. 

Law  of  Mass  Action — The  importance  of  the  relative 
amounts  of  the  reacting  substances  for  the  course  of  a  chemical 
change  was  first  clearly  established  by  Wenzel  and  by  Berth- 
ollet.  The  latter  pointed  out  that  though  under  ordinary 
circumstances  sodium  carbonate  and  calcium  chloride  react 
almost  completely  according  to  the  equation  Na2CO3  -f 
CaCl2  ->  2NaCl  +  CaCO3,  yet  the  sodium  carbonate  found 
on  the  shores  of  certain  lakes  in  Egypt  is  produced  according 
to  the  equation  2NaCl  +  CaCO3  ->  Na2CO3  +  CaCl2,  the 
converse  of  the  first  equation.  In  the  latter  case,  the  sodium 
chloride  is  present  in  solution  in  such  large  excess  that  the  re- 
action proceeds  in  the  direction  indicated  by  the  arrow,  so  that, 
according  to  Berthollet,  an  excess  in  quantity  can  compensate 
for  a  weakness  in  specific  affinity. 

An  important  step  forward  was  made  in  this  subject  by 
Berthelot  and  Pean  de  St.  Gilles  in  1862,  in  the  course  of  an 
investigation  on  the  formation  of  esters  from  acids  and  alcohol. 
For  acetic  acid  and  ethyl  alcohol,  the  reaction  may  be  repre- 
sented by  the  equation 

C2H5OH  +  CH3COOH  ^  CH3COOC2H5  +  H2O. 
If  one   starts  with  equivalent  amounts   of  acid   and  alcohol, 


156        OUTLINES  OF  PHYSICAL  CHEMISTRY 

the  reaction  proceeds  till  about  66  per  cent,  of  the  reacting 
substances  have  been  used  up,  and  then  comes  to  a  standstill. 
Similarly,  if  equivalent  quantities  of  ethyl  acetate  and  water  are 
heated,  the  reaction  proceeds  in  the  reverse  direction  (indicated 
by  the  lower  arrow)  until  34  per  cent,  of  the  compounds  have 
been  used  up  and  the  mixture  finally  obtained  is  of  the  same 
composition  as  when  acid  and  alcohol  are  the  initial  substances. 
A  reaction  of  this  type  is  termed  a  reversible  reaction,  and  the 
facts  are  conveniently  represented  by  the  oppositely-directed 
arrows. 

When,  however,  for  a  fixed  proportion  of  acid,  varying 
amounts  of  alcohol  are  taken,  the  equilibrium  point  is  greatly 
altered,  as  is  shown  in  the  accompanying  table.  The  first  and 
third  columns  show  the  proportion  of  alcohol  present  for  i 
equivalent  of  acetic  acid,  and  the  second  and  fourth  columns 
the  proportion  of  acid  per  cent,  converted  to  ester. 

Ester 
Formed. 

82-8 
88-2 

i'o  6b'5  12*0  93-2 

1*5  77*9  50*0  loo'o 

We  here  measure  the  amount  of  chemical  action  by  the  extent 
to  which  the  acid  is  converted  into  ester,  and  the  table  shows 
very  clearly  the  influence  of  the  mass  of  the  alcohol  on  the 
equilibrium. 

The  influence  of  the  relative  proportions  of  the  reacting 
substances  on  chemical  action  was  thus  clearly  recognised,  but 
was  not  accurately  formulated  till  1867.  In  that  year,  two  Nor- 
wegian investigators,  Guldberg  and  Waage,  enunciated  the  Law 
of  mass  action,  which  may  provisionally  be  expressed  as  follows  : 
The  amount  of  chemical  action  is  proportional  to  the  active  mass 
of  each  of  the  substances  reacting,  active  mass  being  defined  as  the 
molecular  concentration  of  the  reacting  substance.  The  im- 
portant part  of  this  statement  is  that  the  chemical  activity  of 


Equivalents  of 
Alcohol. 

O'2 

Ester 
Formed. 

I9-3 
42'0 

Equivalents  of 
Alcohol. 

2*0 

EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS     157 

a  substance  is  not  proportional  to  the  quantity  present,  but  to 
its  concentration,  or  amount  in  unit  volume  of  the  reaction 
mixture.  The  law  applies  in  the  first  instance  more  particularly 
to  gases  and  substances  in  solution ;  the  active  mass  of  solids 
will  be  considered  later. 

The  "  amount  of  chemical  action  "  exerted  by  a  certain  sub- 
stance can  be  measured  (a)  from  its  influence  on  the  equilibrium, 
as  in  the  formation  of  ethyl  acetate,  just  referred  to ;  (ft)  from 
its  influence  on  the  rate  of  a  chemical  action,  such  as  the  inver- 
sion of  cane  sugar.  The  law  of  mass  action  can  therefore  be 
deduced  from  the  results  of  kinetic  or  equilibrium  experiments. 
Conversely,  once  the  law  is  established,  it  can  be  employed  both 
for  the  investigation  of  rates  of  reaction  and  of  chemical 
equilibria,  and  it  is  the  fundamental  law  in  both  these  branches 
of  physical  chemistry. 

In  the  above  form,  the  law  of  mass  action  cannot  readily  be 
applied,  and  it  will  therefore  be  formulated  mathematically. 
For  purposes  of  illustration,  we  choose  a  reversible  reaction 
between  two  substances  in  which  only  one  molecule  of  each 
reacts ;  a  typical  case  is  the  formation  of  ethyl  acetate  and 
water  from  ethyl  alcohol  and  acetic  acid,  already  referred  to. 
Calling  the  molecular  concentrations  of  the  reacting  substances 
a  and  3,  the  rate  at  which  they  combine  is,  according  to  the  law 
of  mass  action,  proportional  to  a  and  to  b  separately,  and  there- 
fore proportional  to  their  product.  We  may  therefore  write  for 
the  initial  velocity  of  reaction  at  the  time  /0 — 

Rate,0  oc  ab  or  Rate,o  =  kab, 

where  k  is  a  constant — an  affinity  constant — depending  only  on 
the  nature  of  the  substances,  the  temperature,  etc.  As  the  re- 
action proceeds,  the  active  masses  gradually  diminish,  since  the 
original  substances  are  being  used  up  in  producing  the  new 
substances.  If,  after  an  interval  of  time  /,  x  equivalents  of  the 
ester  and  water  have  been  formed,  the  rate  of  the  original 
reaction  will  be 


158        OUTLINES  OF  PHYSICAL  CHEMISTRY 

Rate,  =  k(a-x)(b-x). 

That  this  must  be  so  is  clear  when  one  bears  in  mind  that 
a  and  b  represent  molecular  concentrations,  and  that  for  every 
molecule  of  ester  and  of  water  which  are  formed,  an  equal 
number  of  molecules  of  acid  and  alcohol  must  be  used  up. 
We  have  now  to  take  into  account  the  fact  that  the  substances 
formed  react  to  produce  the  original  substances.  At  the  time 
/,  when  the  concentration  of  the  ester  and  water  is  x,  the  rate 
of  the  reverse  reaction  will  be :  Rate,  =  k^x1,  where  k^  is 
another  affinity  constant.  We  then  have  two  reactions  pro- 
ceeding in  opposite  directions,  the  velocity  of  the  direct  reaction 
is  continually  diminishing  owing  to  diminishing  concentration, 
that  of  the  reverse  reaction  is  continually  increasing  owing  to 
increasing  concentration  of  the  reacting  substances.  A  point 
must  ultimately  be  reached  when  the  velocity  of  the  direct  is 
equal  to  that  of  the  reverse  reaction,  and  the  system  will  no 
longer  change ;  this  is  the  condition  of  equilibrium.  If  the 
particular  value  of  x  under  these  conditions  is  x1  we  have  the 
equations 

Rate  direct  =  k(a  -  x^(b  -  xj  and  rate  reverse  =  k^, 
and  since  these  are  equal 

k(a  -  x^(b  -  tfj)  =  Vi2> 
which  may  be  written 

(a  -  x^)(b  -  xt)  _  k±   _  „ 

—       _         —     XV* 

x-f 

The  facts  are  made  still  clearer  if  we  represent  the  reaction 
as  follows,  the  initial  concentrations  being  represented  on  the 
upper,  and  the  equilibrium  concentrations  on  the  lower  line : — 
Commencement  a  b  o  o 

C2H5OH  +  CH3COOH^CH3COOC2H5  +  H2O 
Equilibrium       a  —  x1         b  -  x1  xt  xl 

It  is  important  to  note  that,  since  K,  which  is  usually  termed 
the  equilibrium  constant,  is  the  ratio  of  the  two  velocity  con- 


EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS     159 

stants,  which  are  independent  of  the  concentration,  the  above 
equation  holds  for  all  concentrations.  Hence,  if  the  equilibrium 
constant  for  any  chemical  change  is  obtained  from  one  experi- 
ment, the  equilibrium  conditions  can  be  calculated  for  any  value 
of  the  original  concentrations.  Numerous  applications  of  this 
equation  are  given  in  the  succeeding  paragraphs. 

When  more  than  one  molecular  equivalent  of  a  compound 
takes  part  in  a  chemical  change,  each  equivalent  must  be  con- 
sidered separately,  as  far  as  the  law  of  mass  action  is  concerned. 

In  order  to  illustrate  this  statement,  we  will  consider  the  com- 
bination of  hydrogen  and  iodine  to  form  hydriodic  acid.  The 
reaction  is  reversible,  and  may  therefore  be  represented  by  the 
equation 

H2  +  I2^HI  +  HI. 

The  rate  of  the  inverse  reaction  =  ^iCfjj,  since  it  is  propor- 
tional to  the  concentration  of  each  of  the  two  mols  of  hydriodic 
acid  and  therefore  to  their  product.  As  the  velocity  of  the 
direct  reaction  =  £CH2Ci2»  we  obtain  for  the  conditions  at 
equilibrium  the  equation 

On-Aa  _k±_  K 

C2HI     =  *  = 

The  general  equation  for  a  reversible  reaction  may  be  written 
in  the  form 


where  «x  molecules  of  the  substance  Aj  react  with  n2  molecules 
of  the  substance  A2  .  .  .  to  form  n^  molecules  of  the  substance 
A/  and  #2'  molecules  of  the  substance  A2'.  The  rates  of  the 
direct  and  reverse  actions  are  represented  by  the  equations  : 
Rate  direct  =*C»;C£  ...  and  rate  invcrse  =  ktftf?*,  .... 
and  in  equilibrium 


A  A    ' 

Al          A2 

The  above  is  the  strict  mathematical  form  of  the  law  of  mass 


160        OUTLINES  OF  PHYSICAL  CHEMISTRY 

action,  which  in  words  may  be  expressed  as  follows  :  At 
equilibrium  the  product  of  the  concentrations  on  one  side,  divided 
by  the  product  of  the  concentrations  on  the  other  side,  is  constant 
at  constant  temperature.  Thus  for  the  reaction  represented  by 
the  equation  :  — 

2FeCl3  +  SnCl2  =  SnCl4  +  2FeCl2 
we  have 

v          CpeCU  CsnCl2 

=     --  ~  -- 


Strict  Proof  of  the  Law  of  Mass  Action—  The  law  of 

mass  action,  the  meaning  of  which  has  been  illustrated  in 
the  previous  paragraphs,  may  be  strictly  proved  by  a  thermo- 
dynamical  method  (Guldberg  and  Waage,  1867),  or  by  a 
molecular-kinetic  method  (van't  Hoff,  1877).  The  latter  proof 
is  comparatively  simple,  and  depends  on  the  assumption  that 
the  rate  of  chemical  change  is  proportional  to  the  number  of 
collisions  between  the  reacting  molecules,  which,  in  sufficiently 
dilute  solution,  will  be  proportional  to  the  respective  concen- 
trations. Taking  again  ester  formation  as  an  example,  the 
velocity  of  the  direct  change  =  £CaiCOh0i  Cacid  and  that  of  the 
reverse  change  =  ^jCester  Cwater.  At  equilibrium,  the  rates  will 
just  balance,  and  therefore 

"^alcohol  '-•'acid  ==  ^i^ester  ^water* 

As  before,  this  equation  may  be  put  in  the  form 

^alcohol  ^acid          *i          -IT 

r  -  r  -  =  T  =     ' 

^ester  Cwater          K 

where  the  respective  concentrations  are  those  under  equilibrium 
conditions,  and  K  is  the  equilibrium  constant. 

It  follows  from  the  assumptions  made  both  in  the  thermo- 
dynamical  and  kinetic  proofs  that  the  law  of  mass  action  holds 
strictly  only  for  very  dilute  solutions,  but  the  experimental 
results  show  that  it  often  holds  with  a  fair  degree  of  accuracy 
even  for  moderately  concentrated  solutions. 


EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS     161 
EQUILIBRIUM  IN  GASEOUS  SYSTEMS 

(a)  Decomposition  of  Hydriodic  Acid  —  A  typical  example 
of  equilibrium  in  a  gaseous  system  is  that  between  hydrogen, 
iodine  and  hydriodic  acid,  investigated  by  Bodenstein.1  The 
reaction,  which  is  represented  by  the  equation  H2  +  I2^  2HI, 
is  a  completely  reversible  one,  the  concentration  at  equilibrium 
being  the  same  whether  one  starts  with  hydrogen  and  iodine 
or  with  hydriodic  acid,  if  the  conditions  otherwise  are  the  same. 

Applying  the  law  of  mass  action,  we  get  at  once 


as  shown  in  the  previous  paragraph. 

It  is  clear  from  the  equation  that  if  from  one  observation  the 
respective  molecular  concentrations  of  iodine,  hydrogen  and 
hydriodic  acid  are  known,  K,  the  equilibrium  constant  at  the 
temperature  in  question,  can  be  calculated. 

The  question  now  arises  as  to  how  the  progress  of  the 
reaction  can  be  followed,  so  that  it  may  be  known  when 
equilibrium  is  attained.  It  is  further  necessary  to  find  a 
method  of  measurement  such  that  the  equilibrium  does  not 
alter  while  the  observations  are  being  made.  In  this  case  it 
happens  that  both  the  direct  and  inverse  reactions  are  extremely 
slow  at  room  temperature,  but  are  fairly  rapid  at  445°,  the  tem- 
perature of  boiling  sulphur.  If  then  the  mixture  is  heated  for 
a  definite  time  at  a  high  temperature  and  then  cooled  rapidly, 
the  respective  concentrations  at  high  temperatures  can  be  deter- 
mined at  leisure  by  analysis.  The  reacting  substances,  in  varying 
proportions,  are  heated  at  a  definite  temperature  in  sealed  glass 
tubes  for  definite  periods,  and  the  amount  of  hydrogen  then 
present  measured  after  absorption  of  the  iodine  and  hydriodic 
acid  by  means  of  potassium  hydroxide. 

For  the  present,  only  results  will  be  considered  in  which  the 
tubes  were  heated  so  long  at  445°  that  equilibrium  was  attained. 
In  one  experiment,  20-55  mols  of  hydrogen  were  heated  with 

1  Zeitsch.  physikal.  Ckem.,  1897,  22,  i. 


II 


1  62        OUTLINES  OF  PHYSICAL  CHEMISTRY 

31-89  mols  of  iodine,  and  it  was  found  that  the  mixture  at 
equilibrium  contained  2*06  mols  of  hydrogen,  13-40  mols  of 
iodine  and  36-98  mols  of  hydriodic  acid  in  the  same  volume. 
Hence  _  [H2][IJ  _  (2-06  x  13-40) 


(36-98)^ 

Equation  (i)  could,  of  course,  be  tested  by  rinding  if  the 
same  value  of  K  is  obtained  for  different  initial  concentrations 
of  the  reacting  substances,  but  it  is  in  some  respects  preferable 
to  calculate  by  means  of  the  equation  the  proportion  of  hydriodic 
acid  formed  at  equilibrium  when  different  initial  concentrations 
of  the  reacting  substances  are  taken,  and  to  compare  the  results 
with  those  actually  observed.  In  the  calculation,  K  is  taken  as 
0*0200  at  445°. 

If  i  mol  of  hydrogen  is  heated  with  a  mols  of  iodine,  and 
2X  mols  of  hydriodic  acid  are  formed,  i  —  x  mols  of  hydrogen 
and  a  —  x  mols  of  iodine  will  remain  behind.  Substituting  in 
equation  (i), 

(i  -  x}(a  -  x) 

-  -  '-\  -  '-  =  K  =  0-0200        .         .       (2) 
4#2 

The  first  and  second  columns  of  the  accompanying  table 
contain  the  initial  concentrations  of  hydrogen  and  iodine 
respectively,  and  the  fourth  and  fifth  columns  the  observed 
and  calculated  concentrations  of  hydriodic  acid  at  equilibrium, 
the  latter  values  being  obtained  from  the  expression 

I  +  a  ~   **  +  a2  ~    ^" 


s 

where   s  =  i  -  4K  =  0-92 
obtained  by  solving  the  quadratic  equation  (2)  above. 

^x  (calc.) 
10*19 

25M 
37-13 
39-01 

39*25 


Ha 

I. 

I2/H2  =  a 

HI  found 

20-57 

5*22 

0-254 

10*22 

20*6 

14-45 

0*702 

25-72 

20-55 

31-89 

I*552 

36-98 

20*41 

52-8 

2  '  ^  7.8 

38-68 

20-28 

67-24 

3*316 

39^2 

EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS     163 

The  close  agreement  between  observed  and  calculated  values 
shows  that  the  law  of  mass  action  applies  in  this  case. 

It  can  easily  be  shown  from  the  fundamental  equation  that 
in  this  case  the  position  of  equilibrium  is  independent  of  the 
pressure  or  of  the  volume.  Calling  a,  b  and  c  the  amounts  of 
hydrogen,  iodine  and  hydriodic  acid  present  at  equilibrium,  the 
concentrations  are  a/V,  &/V  and  <r/V  respectively,  where  V  is 
the  volume  occupied  by  the  mixture.  Substituting  in  the 
general  equation,  we  obtain  able*  =  K  ;  in  other  words,  K  is 
independent  of  the  volume.  Bodenstein  found  that  this  re- 
quirement of  the  theory  was  also  satisfactorily  fulfilled. 

(b)  Dissociation  of  Phosphorus  Pentachloride  —  Another 
instructive  example  of  equilibrium  in  a  gaseous  system  is  that 
between  phosphorous  pentachloride  and  its  products  of  de- 
composition, represented  by  the  equation  PC15  "f.  PC13  +  C12. 
A  decomposition  of  this  type,  in  which  a  chemical  compound 
yields  one  or  more  products,  is  termed  dissociation,  and  the 
student  will  have  met  with  many  examples  of  dissociation  in  his 
earlier  work.  As  before,  on  applying  the  law  of  mass  action, 
we  obtain 


If  we  commence  with  a  molecules  of  PC15,  and  x  molecules 
each  of  PC13  and  C12  are  formed,  the  concentrations  of  PC15, 
PC13  and  C12  at  equilibrium  are  (a  —  x)/Vt  x/V  and  x/~V  re- 
spectively, and,  substituting  in  the  above  equation, 


K. 


(a  -  *)V 

It  will  be  observed  that  the  equilibrium  in  this  case  depends 
on  the  volume,  and  the  larger  the  volume  the  smaller  is  (a  -  x) 
— in  other  words,  the  greater  is  the  dissociation. 

An  important  point  in  connection  with  chemical  equilibrium 
in  general  is  the  effect  of  the  addition  of  excess  of  one  of  the 
products  of  decomposition  (dissociation)  on  the  degree  of 


1  64       OUTLINES  OF  PHYSICAL  CHEMISTRY 

decomposition.  If,  for  example,  a  mols  of  PC15  are  vaporized 
in  a  volume  V  in  which  b  mols  of  PC13  are  already  present,  and 
if  x1  is  the  degree  of  dissociation  of  the  pentachloride  under  these 
conditions,  the  relative  concentrations  of  trichloride,  penta- 
chloride and  chlorine  will  be  b  -f  xlt  a  —  xv  and  xl  respec- 
tively. The  equilibrium  equation  is  therefore 
fa)  (b  +  x,) 


(a  -  *X 

where  K  has  the  same  numerical  value  as  for  the  pentachloride 
alone,  provided  that  the  volume  V  and  the  temperature  are  the 
same.  If  it  is  assumed  that  the  degree  of  dissociation  when 
PC16  is  heated  alone  under  the  same  conditions  is  i  not  more 
than  say  25  per  cent.,  it  is  clear  that  the  proportion  of  undis- 
sociated  compound  cannot  be  very  seriously  increased  by  the 
presence  of  excess  of  PC13.  Hence  when  £,  the  initial  amount 
of  PC13,  is  made  very  large,  xv  the  amount  of  chlorine  present 
at  equilibrium  must  become  very  small  in  order  that  the  pro- 
duct K  (a  -  xj  may  retain  approximately  the  same  value  ;  in 
other  words,  the  dissociation  of  PC15  must  then  be  very  small. 
From  these  considerations  we  deduce  the  following  important 
general  rule  :  The  degree  of  dissociation  of  a  compound  is 
diminished  by  addition  of  excess  of  one  of  the  products  of 
dissociation  provided  that  the  volume  remains  constant. 

Equilibrium  in  Solutions  of  Non-Electrolytes—  As  an 
illustration  of  an  equilibrium  in  solution,  that  between  acid, 
alcohol,  ester  and  water  (p.  156)  may  be  considered  rather 
more  fully.  For  this  equilibrium,  according  to  the  law  of 
mass  action,  we  have 

Cacid  Caicohoi         v 

P  -  P  -    =-  K. 

tester  v-'water 

If  at  the  commencement  a,  b  and  c  mols  of  acid,  alcohol  and 
water  respectively  are  present  in  V  litres,  and  under  equi- 
librium conditions  x  mols  of  water  and  ester  respectively  have 
been  formed,  the  respective  concentrations  are 


EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS     165 
a-x  _b_^.  r        _«£.    r  c  +  x  . 

'-'acid  =       Y      '    ^alc-   ~       V      '    ^ester  *~~  y  >     '-'water  -         y 

whence,  substituting  in  the  above  equation, 
(a-x)(fi-x) 

x(c  +  x) 

In  this  case  also,  the  position  of  equilibrium  is  independent  of 
the  volume. 

The  value  of  K  may  be  obtained  from  the  observation  already 
mentioned,  that  when  acid  and  alcohol  are  taken  in  equivalent 
proportions,  two-thirds  is  changed  to  ester  and  water  under 
equilibrium  conditions.  Hence 


This  equation  may  now  be  employed,  as  in  the  case  of  hydriodic 
acid,  to  calculate  the  equilibrium  conditions  for  varying  initial 
concentrations  of  the  reacting  substances.  As  an  example,  we 
take  the  proportion  of  i  mol  of  acetic  acid  converted  to  ester  by 
varying  proportions  of  alcohol,  when  the  initial  mixture  contains 
neither  ester  nor  water.  The  equation  in  this  case  simplifies  to 

(!-*)(*-*) 

2  ~   fl 


whence  x  =  f  (i  +6-  fi  -  b  +  i).  The  observed  and  cal- 
culated values  of  x  are  given  in  the  table,  and  it  will  be  seen 
that  the  agreement  is  very  satisfactory,  although  the  solution  is 
so  concentrated  that  it  is  scarcely  to  be  expected  that  the  law  of 
mass  action  will  apply  strictly. 


b 

x  (found) 

x  (calc.) 

b 

x  (found) 

x  (calc.) 

°'°5 

0*05 

0*049 

0*67 

0-519 

0-528 

0-08 

0-078 

0-078 

1*0 

0-665 

0*667 

0*18 

0-171 

0*171 

i'S 

0-819 

0*785 

0-28 

0*226 

0*232 

2*0 

0*858 

0*845 

o'33 

0-293 

0*311 

2-24 

0-876 

0*864 

o'5° 

0-414 

0*423 

8-0 

0*966 

°*945 

1  66       OUTLINES  OF  PHYSICAL  CHEMISTRY 

As  regards  the  practical  investigation  of  this  equilibrium,  the 
reacting  substances  are  heated  in  sealed  tubes  at  constant 
temperature  (say  100°)  till  equilibrium  is  attained,  cooled,  and 
the  contents  titrated  with  dilute  alkali,  using  phenolphthalein  as 
indicator.  As  the  concentrations  of  acid  and  alcohol  before  the 
experiment  are  known  and  the  acid  concentration  after  the  at- 
tainment of  equilibrium  is  obtained  from  the  results  of  the 
titration,  the  proportion  of  ester  formed  can  readily  be  calcu- 
lated. 

The  equilibrium  in  salt  solutions  will  be  more  conveniently 
dealt  with  at  a  later  stage  (Chapter  XL). 

Influence  of  Temperature  and  Pressure  on  Chemical 
Equilibrium.  General  —  The  equations  for  chemical  equi- 
librium deduced  by  means  of  the  law  of  mass  action  hold  for 
all  temperatures  provided  that  all  the  components  remain  in  the 
system  :  the  only  effect  of  change  of  temperature  is  to  alter  the 
value  of  the  equilibrium  constant.  The  displacement  of  equi- 
librium is  connected  with  the  heat  liberated  in  the  chemical 
change  by  the  equation  — 


dT  RT2 

which  shows  that  the  rate  of  change  of  the  logarithm  of  the 
equilibrium  constant  with  temperature  is  equal  to  the  heat 
evolved  in  the  complete  reaction  l  divided  by  twice  the  square 
of  the  absolute  temperature  at  which  the  change  takes  place. 

Strictly  speaking,  the  above  equation  holds  only  for  the  dis- 
placement of  equilibrium  due  to  an  infinitely  small  change  of 
temperature  <fT,  and  must  be  integrated  before  it  can  be  applied 
to  a  concrete  case.  This  can  readily  be  done  on  the  assumption 
that  Q  remains  constant  between  the  two  temperatures,  which 
is  in  general  only  approximately  true.  Integration  between  the 
absolute  temperatures  Tx  and  T2  gives  on  this  assumption 


log*,  -  log«K2  =  - 

1  The  negative  sign  is  taken  in  order  that  Q  may  denote  the  heat  evolved 
in  the  forward  reaction  (from  left  to  right). 


EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS     167 

in  which  Kx  and  K2  are  the  equilibrium  constants  at  T:  and  T2 
respectively.  When  transformed  to  ordinary  logarithms  (by 
dividing  by  2-3026)  and  R  is  put  =  1*99  (p.  27),  the  above 
equation  is  obtained  in  the  more  convenient  form — 

.  .          (2) 

In  this  equation,  Q  refers  only  to  the  heat  used  in  doing 
internal  work,  and  does  not  include  that  used  in  external  work 
(p.  141).  It  applies,  therefore,  in  the  first  instance,  only  to 
systems  in  which  there  is  no  change  of  volume,  and  if  there  is 
expansion  or  contraction,  the  corresponding  correction  must  be 
applied  (p.  27).  The  equation  shows  that  Q  may  be  calculated 
when  the  equilibrium  constants  for  two  near  temperatures,  Tl 
and  T2,  are  known.  Conversely,  when  the  heat  change  in  a 
chemical  reaction  and  the  equilibrium  constant  for  any  one 
temperature  are  known,  the  condition  of  equilibrium  at  any  other 
temperature  may  be  calculated.  The  equation  is  particularly 
useful  for  the  indirect  determination  of  the  heat  of  reaction  at 
high  temperatures  (in  gas  reactions,  for  example)  when  the 
direct  calorimetric  determination  is  difficult  or  impossible. 

As  an  example  of  the  application  of  the  general  equation  (2), 
the  heat  of  dissociation,  Q,  for  hydrogen  sulphide,  represented 
by  the  equation  2H2S;±  2H2  +  S2,  will  be  calculated.  Ac- 
cording to  Preuner,  the  equilibrium  constant  K  of  the  equation 

fH  i2rs  i 

L    2  ^  2   =  K,  has  the  value  2-90  x  io~5  at  1220°  abs.  and 

Ltt2oJ 

10*4  x  io~5at  1320°  abs.  Hence,  substituting  in  equation 
(2),  we  have 

10*4  x  io~5  _  Q        (1320  -  1220) 

°10  2*90  x  io~5  4'5^i  '  (1320  x   1220) 

and  Q  =  -  41,000  cal.  approximately. 

A  specially  interesting  case  is  that  in  which  there  is  no  heat 
change  when  the  first  system  changes  to  the  second.  Since  in 
this  case  Q  =  o,  the  right-hand  side  of  equation  (i)  becomes 
zero,  and  therefore  there  should  be  no  displacement  of  equili- 


1 68       OUTLINES  OF  PHYSICAL  CHEMISTRY 

brium  with  temperature.  The  condition  of  zero  heat  of  reaction 
is,  as  has  already  been  pointed  out  (p.  145),  approximately  ful- 
filled in  ester  formation,  and  in  accordance  with  this,  Berthelot 
found  that  at  10°  65-2  per  cent,  of  the  acid  and  alcohol  change 
to  ester  and  at  220°  66*5  per  cent.;  the  displacement  of 
equilibrium  with  temperature  is  therefore  slight. 

There  are  certain  rules  of  great  importance  which  show 
qualitatively  how  the  equilibrium  is  displaced  with  changes  of 
temperature  and  pressure.  If  Q  is  the  heat  developed  when 
the  system  A  changes  to  the  system  B,  and  is  positive,  then 
with  rise  of  temperature  A  increases  at  the  expense  of  B  ;  con- 
versely, if  Q  is  negative,  B  increases  with  rise  of  temperature 
at  the  expense  of  A.  These  statements  may  be  summarised  as 
follows :  At  constant  volume  increase  of  temperature  favours 
the  system  formed  under  heat  absorption  and  conversely. 

As  an  example,  we  may  take  nitrogen  peroxide,  N2O4  ^  2NO2, 
for  which  the  change  represented  by  the  lower  arrow  is  attended 
with  the  liberation  of  a  large  amount  (12,600  cal.)  of  heat. 
Increase  of  temperature  favours  the  reaction  for  which  heat  is 
absorbed,  in  this  case  the  reaction  represented  by  the  upper 
arrow,  so  that  as  the  temperature  rises  N2O4  is  split  up  more 
completely  into  NO2  molecules. 

Another  interesting  example  is  the  relationship  between 
oxygen  and  ozone,  represented  by  the  equation  2O8  =  3O2  + 
2  x  29,600  cal.  The  equilibrium  for  the  reaction  2O3^t3O2 
is  very  near  the  oxygen  side  at  the  ordinary  temperature,  but 
increase  of  temperature  must  displace  it  in  the  direction  repre- 
sented by  the  lower  arrow,  since  under  these  circumstances  heat 
is  absorbed ;  in  other  words,  ozone  becomes  increasingly  stable 
as  the  temperature  rises.  The  experimental  results  so  far 
obtained  are  in  satisfactory  agreement  with  the  theory.1 

1  Compare  Fischer  and  Marx,  Berichte,  1907,  40,  443.  At  first  sight 
this  appears  to  be  in  contradiction  to  the  well-known  fact  that  when  a 
mixture  of  oxygen  and  ozone  is  heated  to  250°  the  ozone  is  practically 
destroyed.  It  must  be  remembered,  however,  that  the  mixture  contains 
far  too  much  ozone  for  equilibrium,  but  owing  to  the  low  temperature  it 
attains  its  true  equilibrium  very  slowly.  At  250°,  however,  the  attainment 
of  equilibrium  is  fairly  rapid. 


EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS     169 

From  the  above  considerations  we  conclude  that  endothermic 
compounds,  such  as  ozone,  acetylene  and  carbon  disulphide, 
become  increasingly  stable  as  the  temperature  rises,  whilst 
exothermic  compounds  undergo  further  dissociation. 

A  similar  law  can  be  enunciated  for  the  effect  of  pressure  on 
equilibrium  as  follows  :  On  increasing  the  pressure  at  constant 
temperature  the  equilibrium  is  displaced  in  the  direction  in  which 
the  volume  diminishes.  Taking  as  an  illustration  the  gaseous 
equilibrium,  PC15^±PC13  +  C12  in  which  the  upper  arrow 
indicates  the  direction  of  increase  of  volume,  the  rule  indicates 
that  increase  of  pressure  will  displace  the  equilibrium  to  the 
left,  whilst  decrease  of  pressure  will  favour  the  reverse  change. 
As  is  well  known,  these  deductions  are  in  complete  accord  with 
the  experimental  facts. 

For  reactions  not  attended  by  any  appreciable  change  of 
volume,  such  as  the  decomposition  of  hydriodic  acid  at  high 
temperatures,  the  equilibrium  should  not  be  altered  by  change 
of  volume,  a  conclusion  borne  out  by  experiment  (p.  163). 

Le  Chatelier's  Theorem — Le  Chatelier  has  pointed  out 
that  the  rules  above  referred  to  with  regard  to  the  effect  of 
changes  of  temperature  and  pressure  on  equilibria  are  special 
cases  of  a  much  more  general  law  which  may  be  enunciated 
as  follows  :  When  one  or  more  of  the  factors  determining  an  equi- 
librium are  altered,  the  equilibrium  becomes  displaced  in  such  a 
way  as  to  neutralize,  as  far  as  possible,  the  effect  of  the  change. 
A  little  consideration  will  show  that  this  rule  affords  a  satisfac- 
tory interpretation  of  all  the  phenomena  just  mentioned. 

Relation  between  Chemical  Equilibrium  and  Tem- 
perature. Nernst's  Yiews — Although  the  van't  Hoff 
equation  connecting  equilibrium  and  temperature  enables  us 
to  calculate  the  position  of  equilibrium  at  different  tempera- 
tures when  the  position  of  equilibrium  at  one  temperature 
and  the  heat  of  reaction  are  known,  it  has  not  untilv  quite 
recently  been  possible  to  calculate  chemical  equilibria  from 
thermal  and  thermochemical  data  alone.  Within  the  last 


1  7o       OUTLINES  OF  PHYSICAL  CHEMISTRY 

two  or  three  years,  the  latter  problem  appears  to  have  been 
to  a  great  extent  solved  by  Nernst.1  The  fundamental  as- 
sumption, on  the  basis  of  which  it  has  been  found  possible 
to  deduce  formulae  connecting  the  equilibrium  in  a  system 
with  the  thermal  data  characteristic  of  the  reacting  substances, 
is  that  the  free  energy,  A,  and  the  total  heat  of  reaction,  Q, 
are  not  only  equal  at  the  absolute  zero,  as  already  pointed  out 
(p.  152),  but  their  values  coincide  completely  in  the  immediate 
vicinity  of  that  point.  It  is  evident  that  this  assumption  cannot 
be  tested  directly,  but  the  fact  that  the  formulae  deduced  on 
this  basis  have  been  to  a  great  extent  confirmed  by  experiment  2 
goes  far  to  justify  it. 

There  can  be  no  doubt  that  the  results  just  described  con- 
stitute one  of  the  most  important  advances  in  physics  and 
chemistry  of  recent  years.  It  is  beyond  the  scope  of  the 
present  book  to  discuss  the  question  more  fully,  but  it  may 
be  mentioned  that  the  theory  not  only  admits  of  the  calcula- 
tion of  equilibria  in  homogeneous  and  heterogeneous  systems 
from  thermal  data,  but  also  gives  a  formula  representing  the 
variation  of  vapour  pressure  with  temperature. 

Practical  Illustrations  —  The  law  of  mass  action  may  be 
illustrated  most  conveniently  by  the  action  of  water  on  bismuth 
chloride,  represented  by  the  equation 
BiCl   + 


When  dilute  hydrochloric  acid  is  added  to  a  mixture  of  the 
salt  and  water,  the  equilibrium  is  displaced  in  the  direction 
represented  by  the  lower  arrow,  and  a  homogeneous  solution  is 
obtained.  If  excess  of  water  is  added  to  this  solution,  the 
equilibrium  is  displaced  in  the  direction  represented  by  the 
upper  arrow,  and  a  precipitate  of  bismuth  oxychloride  is  formed. 

The  law  may  also  be  illustrated  qualitatively  by  the  inter- 
action of  ferric  chloride  and  ammonium  thiocyanate  to  form 

1  Nernst,  Applications   of  Thermodynamics  to  Chemistry.      London  ; 
Constable,  1907.     Annual  Reports,  Chemical  Society,  1906,  pp.  20-22. 

2  Nernst,  loc.  cit, 


EQUILIBRIUM  IN  HOMOGENEOUS  SYSTEMS     171 

blood-red  ferric  thiocyanate.1  This  reaction  is  of  particular 
interest,  as  it  was  one  of  the  first  reversible  reactions  to  be 
systematically  investigated  (J.  H.  Gladstone,  iSss).2  The 
equation  representing  the  reaction  is  as  follows : — 

FeCl3  +  3NH4CNS  ^  Fe(CNS)3  +  3NH4C1. 

Solutions  of  the  salts  are  first  prepared;  the  thiocyanate 
solution  contains  3-7  grams  of  the  salt  to  100  c.c.  of  water, 
and  the  ferric  chloride  solution  3  grams  of  the  commercial 
salt  and  12 '5  c.c.  of  concentrated  hydrochloric  acid  to  100 
c.c.  of  water.  5  c.c.  of  each  of  the  solutions  are  added  to 
2  litres  of  water  and  the  solution  divided  between  four  beakers. 
The  solutions  are  pale-red  in  colour,  as  the  equilibrium  lies 
considerably  towards  the  left-hand  side.  To  the  contents  of 
two  of  the  beakers  are  added  5  c.c.  of  the  ferric  chloride  and 
the  thiocyanate  solution  respectively,  and  it  will  be  observed 
that  the  solutions  become  deep  red,  owing  to  the  displace- 
ment of  the  equilibrium  in  the  direction  of  the  upper  arrow. 
On  the  other  hand,  the  addition  of  50  c.c.  of  a  concentrated 
solution  of  ammonium  chloride3  to  the  solution  in  the  third 
beaker  makes  it  practically  colourless,  the  equilibrium  being 
displaced  in  the  direction  of  the  lower  arrow,  in  accordance 
with  the  law  of  mass  action. 

1  Lash  Miller  and  Kenrick,  J.  Amer,  Chem.  Soc.,  22,  291. 

2  Phil.  Trans.  Roy.  Soc.,  1855,  179. 

3  Strictly  speaking,  all  the  solutions  should  be  made  up  to  the  same 
volume  in  each  case,  but  for  qualitative  purposes  the  method  described  is 
sufficiently  accurate.     The  deep-red  colour  is  presumably  due  to  the  for- 
mation ot   non-ionised  ferric  thiocyanate  (p.   260) ;    it  cannot  be  due  to 
Fe*"  or  to  CNS1  ions,  which  are  practically  colourless. 


CHAPTER  VIII 

HETEROGENEOUS  EQUILIBRIUM.     THE  PHASE 
RULE 

General — In  contrast  to  homogeneous  systems,  in  which 
the  composition  is  uniform  throughout,  heterogeneous  systems 
are  made  up  of  matter  in  different  states  of  aggregation.  The 
separate  portions  of  matter  in  equilibrium  are  usually  termed 
phases  ;  each  phase  is  itself  homogeneous,  and  is  separated  by 
bounding  surfaces  from  the  other  phases.  Liquid  water  in 
equilibrium  with  its  vapour  is  a  heterogeneous  system  made 
up  of  two  phases,  the  equilibrium  in  this  case  being  of  a 
physical  nature.  Another  heterogeneous  equilibrium,  formed 
by  calcium  carbonate  with  its  products  of  dissociation,  consists 
of  three  phases,  two  of  which  are  solid,  calcium  carbonate  and 
calcium  oxide,  and  one  gaseous.  A  still  more  complicated  case 
is  the  equilibrium  between  a  solid  salt,  its  saturated  solution, 
and  vapour,  made  up  of  a  solid,  a  liquid  and  a  gaseous  phase. 
It  should  be  remembered  that  though  each  phase  must  be 
homogeneous,  both  as  regards  chemical  and  physical  pro- 
perties, it  may  be  chemically  complex.  For  example,  a  mixture 
of  gases  only  forms  a  single  phase,  since  gases  are  miscible  in 
all  proportions.  Further,  a  phase  may  be  of  variable  composi- 
tion, thus  a  solution  only  constitutes  one  phase,  although  it 
may  vary  greatly  in  concentration. 

Application  of  Law  of  Mass  Action  to  Heterogeneous 
Equilibrium — It  has  already  been  shown  that  equilibria  in 
homogeneous  systems  may  be  dealt  with  satisfactorily  by 

172 


HETEROGENEOUS  EQUILIBRIUM  173 

means  of  the  law  of  mass  action,  provided  that  the  molecular 
condition  of  the  reacting  substances  is  known.  The  matter  is, 
however,  somewhat  more  complicated  for  heterogeneous  equi- 
libria, more  particularly  when  solid  substances  are  present,  as 
in  the  equilibrium  between  calcium  carbonate,  calcium  oxide 
and  carbon  dioxide  already  referred  to.  Debray,  who  investi- 
gated this  system  very  carefully,  showed  that,  just  as  water  at  a 
definite  temperature  has  a  definite  vapour  pressure,  independent 
of  the  amount  of  liquid  present,  there  is  a  definite  pressure  of 
carbon  dioxide  over  calcium  carbonate  and  oxide  at  a  definite 
temperature,  independent  of  the  amount  or  the  relative  propor- 
tions of  the  solids  present.  The  question  now  arises  as  to 
how  the  law  of  mass  action  is  to  be  applied  to  systems  in 
which  solids  are  present.  This  problem  was  solved  by  Guld- 
berg  and  Waage,  who  found  that  the  experimental  results,  such 
as  those  for  the  dissociation  of  calcium  carbonate,  were  satis- 
factorily represented  on  the  assumption  that  the  active  mass  of 
a  solid  substance  at  a  definite  temperature  is  constant,  i.e.,  inde- 
pendent of  the  amount  of  solid  present. 

It  was  not  at  first  clear  what  physical  meaning  is  to  be 
attached  to  this  statement,  but  Nernst  pointed  out  that  for 
any  such  system  it  was  sufficient  to  consider  the  equilibrium 
in  the  gaseous  phase,  the  active  mass  of  a  solid  being  repre- 
sented as  its  concentration  in  the  gaseous  phase.  In  other 
words,  a  solid,  like  a  liquid,  may  be  regarded  as  having  a 
definite  vapour  pressure  at  a  definite  temperature,  independent 
of  its  amount.  At  first  sight  it  may  seem  surprising  to  ascribe 
a  definite  vapour  pressure  to  such  a  substance  as  calcium  oxide, 
but  it  is  well  known  that  solids  like  bismuth  and  cadmium  have 
definite  vapour  pressures  at  moderate  temperatures,  and  there 
is  every  reason  for  supposing  that  the  diminution  of  vapour 
pressure  with  fall  of  temperature  is  continuous.  There  is  now 
no  difficulty  in  applying  the  law  of  mass  action  to  equilibria 
in  which  solid  substances  are  concerned,  for  example,  to  the 
dissociation  of  calcium  carbonate.  For  convenience,  we  will 


174       OUTLINES  OF  PHYSICAL  CHEMISTRY 

use  the  partial  pressures,  p,  of  the  components  in  the  gaseous 
phase  as  representing  the  active  masses.1     We  then  obtain 

•  COo 


whence  /Co2  =    f  ^aC°3  =  constant. 


Otherwise  expressed,  since  all  the  factors  on  the  right-hand 
side  of  the  equation  are  constant  at  constant  temperature,  the 
vapour  pressure  of  carbon  dioxide  must  be  constant,  which  is 
in  accordance  with  the  experimental  facts. 

It  is  clear  from  the  form  of  the  equation  that  the  pressure 
remains  constant  only  within  limits  of  temperature  such  that 
both  calcium  carbonate  and  oxide  are  present.  If  the  tem- 
perature is  so  high  that  no  calcium  carbonate  is  present,  the 
pressure  is  no  longer  denned,  but  depends  on  the  size  of  the 
vessel,  etc. 

Dissociation  of  Salt  Hydrates  —  Other  interesting  examples 
of  heterogeneous  equilibrium  are  those  between  water  vapour  and 
salts  with  water  of  crystallisation.  If,  for  example,  crystallised 
copper  sulphate,  CuSO4,  5H2O  is  placed  in  a  desiccator  over 
concentrated  sulphuric  acid  at  50°,  it  gradually  loses  water  and 
finally  only  the  anhydrous  sulphate  remains.  If  arrangements 
are  made  for  continuously  observing  the  pressure  during  dehyd- 
ration, it  will  be  found  to  remain  constant  at  47  mm.  until  the 
salt  has  lost  two  molecules  of  water,  it  then  drops  to  30  mm. 
and  remains  constant  until  other  two  molecules  of  water  have 
been  lost,  when  it  suddenly  drops  to  4*4  mm.  and  remains 
constant  till  dehydration  is  complete.  The  explanation  of  the 
successive  constant  pressures  observed  during  dehydration  is 
similar  to  that  already  given  for  the  constant  pressure  of  carbon 
dioxide  over  calcium  carbonate  and  oxide.  At  50°  the  hydrates 
CuSO4,  5H2O  and  CuSO4,  3H2O  are  in  equilibrium  with  a 

1  The  partial  pressure  of  a  gas  is  proportional  to  the  number  of  particles 
present  per  unit  volume  and  therefore  to  its  molecular  concentration  or 
active  mass  (cf.  p.  156). 


HETEROGENEOUS  EQUILIBRIUM  175 

pressure  of  aqueous  vapour  =  47  mm.,  and  as  long  as  any  of  the 
pentahydrate  is  present,  the  pressure  necessarily  remains  con- 
stant. When,  however,  all  the  pentahydrate  is  used  up,  the 
trihydrate  begins  to  dehydrate,  giving  rise  to  a  little  of  the 
monohydrate,  CuSO4,  H2O.  As  a  new  substance  is  then  taking 
part  in  the  equilibrium,  the  pressure  of  aqueous  vapour  neces- 
sarily alters,  and  remains  at  the  new  value  until  the  trihydrate  is 
used  up.  The  successive  equilibria  are  represented  by  the 
following  equations : — 

I.  CuS04,  5H2O^CuS04,  3H20  +  2H2O. 
II.  CuS04,  3H2O^CuS04,  H20  +  2H2O. 
III.  CuSO4,  H2O^CuSO4  +  H2O. 

By  applying  the  law  of  mass  action  to  any  of  the  above 
equations,  it  may  easily  be  shown  that  the  pressure  of  aqueous 
vapour  must  be  constant  at  constant  temperature.  Putting  the 
partial  pressures  of  the  pentahydrate  and  the  trihydrate  as  P1 
and  P2  respectively,  we  have  from  equation  I. : — 

£?!  =  ^P2/2H2o. 

kP 

whence /2H2o  =  TIT  =  constant. 
*i"2 

It  is  important  to  realise  clearly  that  the  observed  pressure  is 
not  due  to  any  one  hydrate,  it  is  only  definite  and  fixed  when 
both  hydrates  are  present. 

The  tension  of  aqueous  vapour  over  hydrates,  like  the  vapour 
pressure  of  water,  in  creases  rapidly  with  the  temperature.  This 
is  illustrated  in  the  following  table,  in  which  the  vapour  pressures 
(in  mm.)  over  a  mixture  of  Na2HPO4,  yH2O  and  Na2HPO4, 
and  those  of  water  at  the  same  temperatures,  are  given  : — 

Temperature          .         .  12-3°  16-3°  207°     24-9°  31 '5°  36-4°  40-0° 

Na2HPO4  +  o-7H2O     .  4-8  6-9  9-4    "12-9  21*3  30-5  4i-2 

Water  ....  10-6  13-8  18-1      23-4  34-3  45-i  54-g 

Ratio  salt/water    .         .  0-46  0-50  0-52      0-55  0-62  0-68  075 

The  results  throw  light  on  the  question  of  the  efflorescence 
(giving  up  of  water)  and  deliquescence  (absorption  of  water)  of 


176        OUTLINES  OF  PHYSICAL  CHEMISTRY 

hydrated  salts  in  contact  with  the  atmosphere.  If  a  hydrate 
(in  the  presence  of  the  next  lower  hydrate)  has  a  higher  vapour 
pressure  than  the  ordinary  pressure  of  aqueous  vapour  in  the 
atmosphere,  it  will  lose  water  and  form  a  lower  hydrate.  For 
example,  the  salt  Na2HPO4,  i2H2O  has  a  vapour  pressure  of 
over  1  8  mm.  at  25°,  which  is  greater  than  the  average  pressure 
of  aqueous  vapour  in  the  atmosphere  at  that  temperature,  though 
less  than  the  saturation  pressure  (see  table),  and  therefore  the 
salt  is  efflorescent  under  ordinary  conditions.  On  the  other 
hand,  the  vapour  tension  of  the  heptahydrate  at  25°  is  only 
13  mm.  and  it  is  therefore  stable  in  air.  The  table  shows  that 
the  ratio  of  the  vapour  pressure  of  a  hydrate  to  that  of  water 
increases  rapidly  with  the  temperature  and  ultimately  it  becomes 
greater  than  unity  ;  the  vapour  tension  of  the  hydrate  is  then 
greater  than  that  of  water. 

Dissociation  of  Ammonium  Hydrosulphide  —  Solid 
ammonium  hydrosulphide  partly  dissociates  on  heating  into 
ammonia  and  hydrogen  sulphide,  according  to  the  equation 
NH4HS^NH3  +  H2S.  This  equilibrium  is  of  a  different  type 
to  those  already  mentioned,  as  a  solid  dissociates  into  two 
gaseous  components.  Representing  molecular  concentrations  as 
partial  pressures,  we  obtain,  on  applying  the  law  of  mass  action, 


=K,or/NH3^H2s=  K/NH4HS  =  constant, 

since  the  partial  pressure  of  solid  ammonium  sulphide  is 
constant  at  constant  temperature. 

The  equation  indicates  that  the  product  of  the  partial 
pressures  of  the  two  gases  is  constant  at  constant  temperature. 

When  the  gases  are  obtained  by  heating  ammonium  hydro- 
sulphide,  they  are  necessarily  present  in  equivalent  amount  and 
exert  the  same  partial  pressure.  The  above  formula  may, 
however,  be  tested  by  adding  excess  of  one  of  the  products 
of  dissociation  to  the  mixture.  This  was  done  by  Isambert, 
with  the  result  indicated  in  the  following  table,  which  holds  for 
25*1°;  the  volume  being  kept  constant  throughout;  — 


HETEROGENEOUS  EQUILIBRIUM  177 


250-5  250-5  62,750 

2o8'o  294-0  60,700 

453-0  143-0  64,800 

In  the  first  experiment  the  gases  are  present  in  equivalent 
proportions,  in  the  second  experiment  excess  of  hydrogen 
sulphide,  in  the  third  excess  of  ammonia  have  been  added. 
The  results  indicate  that  the  product  of  the  pressures  is  con- 
stant within  the  limits  of  experimental  error,  as  the  theory 
indicates,  and,  further,  that  addition  of  excess  of  one  of  the 
products  of  dissociation  diminishes  the  amount  of  the  other,  as 
already  shown  for  phosphorus  pentachloride  (p.  163). 

Analogy  between  Solubility  and  Dissociation  —  There 
is  a  very  close  analogy  between  the  solubility  of  solids  in 
liquids  and  the  equilibrium  phenomena  just  considered,  more 
particularly  the  dissociation  of  salt  hydrates.  In  both  cases 
there  is  equilibrium  between  the  solid  as  such  and  the  same  sub- 
stance in  the  other  (gaseous  or  liquid)  phase.  We  have  already 
seen,  in  the  case  of  the  hydrates  of  copper  sulphate,  that  the 
vapour  pressure  (i.e.,  the  concentration  of  vapour  in  the  gas 
space)  depends  on  the  composition  of  the  solid  phases,  and 
it  is  then  easy  to  see  that  the  solubility  of  sodium  sulphate 
(its  concentration  in  the  liquid  phase)  must  also  depend  on 
the  composition  of  the  solid  phase.  The  solubility  alters  when 
the  solid  decahydrate  changes  to  the  anhydrous  salt,  just  as 
does  the  vapour  pressure  when  copper  sulphate  pentahydrate 
disappears.  A  further  analogy  between  the  two  phenomena  is 
that  just  as  the  addition  of  an  indifferent  gas  to  the  gas  phase 
does  not  alter  the  equilibrium,  except  in  so  far  as  the  volume  is 
changed,  so  the  addition  of  an  indifferent  substance  to  a  solu- 
tion does  not  greatly  affect  the  solubility  of  the  original  solute. 

Distribution    of   a  Solute  between  two  Immiscible 

Liquids  —  The  distribution  of  a  solute  such  as  succinic  acid 

between  two  immiscible  liquids  such  as  ether  and  water  exactly 

corresponds  with  the  distribution  of  a  substance  between  the 

12 


178       OUTLINES  OF  PHYSICAL  CHEMISTRY 

liquid  and  gas  phase  (p.  83),  and  therefore  the  rules  already 
mentioned  for  the  latter  equilibrium  apply  unchanged  to  the 
former.  The  most  important  results  may  be  expressed  as 
follows  (Nernst) : — 

(1)  If  the  molecular  weight  of  the  solute  is  the  same  in  both 
solvents,  the  distribution  coefficient  (the  ratio  of  the  concentra- 
tions in  the  two  solvents  after  equilibrium  is  attained)  is  con- 
stant at  constant  temperature  (Henry's  law). 

(2)  In  presence  of  several  solutes,  the  distribution  for  each 
solute  separately  is  the  sarUe  as  if  the  others  were  not  present 
(Dalton's  law  of  partial  pressures). 

The  first  rule  may  be  illustrated  by  the  results  obtained  by 
Nernst  for  the  distribution  of  succinic  acid  between  ether  and 
water,  which  are  given  in  the  table : — 

Ca  (in  water)  C2  (in  ether)  Cj/Cg 

0*024  0*0046  5*2 

0-070  0-013  5'4 

0"I2I  0-022  5'4 

The  results  were  obtained  by  shaking  up  varying  quantities 
of  succinic  acid  with  10  c.c.  of  water  and  10  c.c.  of  ether  in 
a  separating  funnel,  and  determining  the  concentrations  of  acid 
in  the  two  layers  after  they  had  separated  completely.  The 
fact  that  the  ratio  C!/C2  is  approximately  constant  shows  that 
Henry's  law  applies. 

When  the  molecular  weight  of  the  solute  is  not  the  same 
in  both  solvents,  the  ratio  of  the  concentrations  is  no  longer 
constant,  and,  conversely,  if  the  ratio  of  the  concentrations  is 
not  constant  at  constant  temperature,  the  molecular  weight 
cannot  be  the  same  in  both  solvents.  This  is  illustrated  by  the 
following  results  obtained  by  Nernst  for  the  distribution  of 
benzoic  acid  between  water  and  benzene : — 

Cj  (in  water)  C2  (in  benzene)  GI/CS  ci/  \/c£ 

0*0150  0*242  0*062  0*0305 

0*0195  0*412  0*048  0*0304 

0*0289  0*970  0*030  0*0293 


HETEROGENEOUS  EQUILIBRIUM  179 

As  the  table  shows,  the  ratio  Cj/Cg  is  not  even  approximately 
constant,  but  on  the  other  hand,  the  ratio  Cj/  *JCZ  is  constant 
(fourth  column).  A  little  consideration  shows  that  this  is 
connected  with  the  fact  already  mentioned,  that  whilst  benzoic 
acid  has  the  normal  molecular  weight  in  water,  in  benzene  it  is 
present  almost  entirely  as  double  molecules  (p.  124).  In  this 
case  also  we  may  assume  that  there  is  a  constant  ratio  between 
the  concentrations  of  the  simple  molecules  in  the  two  phases, 
and  as  it  may  easily  be  shown  (p.  267)  that  the  concentration 
of  the  simple  molecules  in  benzene  is  proportional  to  the  square 
root  of  the  total  concentration,  the  results  are  in  accord  with 
the  theory. 

The  Phase  Rule,  Equilibrium  between  Water,  Ice 
and  Steam — In  the  previous  sections  of  this  chapter,  it  has 
been  shown  that  many  heterogeneous  equilibria  can  be  dealt 
with  satisfactorily  by  means  of  the  law  of  mass  action.  This 
holds  not  only  for  phases  of  constant  composition,  but  within 
limits  also  for  phases  of  variable  composition,  such  as  solutions. 
With  reference  to  dilute  solutions  there  is,  of  course,  no  difficulty, 
as  the  active  mass  of  the  solute  is  proportional  to  its  concentra- 
tion. This  is  not  the  case,  however,  for  strong  solutions,  and 
the  application  of  the  law  of  mass  action  to  these  is  attended 
with  considerable  uncertainty. 

As  far  back  as  1874,  a  complete  method  for  the  representa- 
tion of  chemical  equilibria  was  developed  by  the  American 
physicist,  Willard  Gibbs,  which  has  come  to  be  known  as  the 
phase  rule.  The  first  point  to  notice  with  regard  to  this  method 
is  that  it  is  entirely  independent  of  the  molecular  theory ;  the 
composition  of  a  system  is  determined  by  the  number  of  in- 
dependently variable  constituents,  which  Gibbs  terms  components. 
He  then  goes  on  to  determine  the  number  of  "  degrees  of  free- 
dom "  of  a  system  from  the  relation  between  the  number  of 
components  and  the  number  of  phases.  It  is  for  this  reason 
that  his  method  of  classification  is  termed  the  phase  rule. 

In  order  to  make  clear  the  meaning  of  the  terms  employed 
it  will  be  well,  before  enunciating  the  rule,  to  illustrate  them  by 


Solid 


1 80       OUTLINES  OF  PHYSICAL  CHEMISTRY 

means  of  a  very  simple  case,  namely  water.  As  regards  the 
equilibrium  in  this  case,  we  may,  according  to  the  conditions 
of  the  experiment,  have  one,  two  or  more  phases  present. 
Thus,  under  ordinary  conditions  of  temperature  and  pressure, 
there  are  two  phases,  water  and  water  vapour,  in  equilibrium. 
This  equilibrium  is  represented  in  the  accompanying  diagram 
by  the  line  OA  (Fig.  22),  temperature  being  measured  along 
the  horizontal  and  pressure  along  the  vertical  axes.  It  is  only 
at  points  on  the  curve  that  there  is  equilibrium.  If,  for  example, 
the  pressure  is  kept  below  that  represented  by  a  point  on  the 

curve  OA  (by  continuously 
increasing  the  volume)  the 
whole  of  the  water  will  be 
converted  to  vapour  ;  if,  on 
the  other  hand,  it  is  kept  at  a 
point  a  little  above  the  curve 
at  a  definite  temperature,  the 
O  vapour  whole  of  the  vapour  will  ulti- 

mately liquefy.  When  the 
temperature  is  a  little  below 
o°,  only  ice  and  vapour  are 

Temperature-*  present,  and   the  equilibrium 

FIG.  22.  between  them  is  represented 

on  the   diagram   by  the   line 
OC,  which  is  not  continuous  with  OA. 

The  two  curves  meet  at  O,  and  O  is  the  point  at  which  ice 
and  water  are  in  equilibrium  with  water  vapour.  It  is  easy  to 
see  that  at  this  point  ice  and  water  have  the  same  vapour 
pressure.  If  this  were  not  so,  vapour  would  distil  from  the 
phase  with  the  higher  vapour  pressure  to  that  with  the  lower 
vapour  pressure  till  the  first  phase  was  entirely  used  up,  a 
result  in  contradiction  with  the  fact  that  the  two  phases  remain 
in  equilibrium  at  this  point.  Since  o°  is  the  temperature  at 
which  ice  and  water  are  in  equilibrium  with  their  vapour  under 
atmospheric  pressure,  and  as  pressure  lowers  the  melting-point 


HETEROGENEOUS  EQUILIBRIUM  181 

of  ice,  the  point  O,  at  which  the  two  phases  are  in  equilibrium 
under  the  pressure  of  their  own  vapour  (about  4*6  mm.),  must 
be  a  little  above  o° ;  the  actual  value  is  +  0*007°  C.  The 
diagram  is  completed  for  stable  phases  by  drawing  the  line  OB, 
which  represents  the  effect  of  pressure  on  the  melting-point  of 
ice ;  the  line  is  inclined  towards  the  pressure  axis  because  in- 
creased pressure  lowers  the  melting-point. 

The  point  O  is  termed  a  triple  point,  because  there,  and 
there  only,  three  phases  are  in  equilibrium.  At  points  along 
the  curves  two  phases  are  in  equilibrium,  and  under  the  con- 
ditions in  the  intermediate  spaces  only  one  phase  is  present,  as 
the  diagram  shows. 

So  far,  only  stable  conditions  have  been  considered,  but 
unstable  conditions  may  also  occur.  Thus  water  does  not 
necessarily  freeze  at  o° ;  if  dust  is  carefully  excluded,  it  is  pos- 
sible to  follow  the  vapour  pressure  curve  for  some  degrees 
below  zero.  The  part  of  the  curve  thus  obtained  is  represented 
by  the  dotted  line  OA'  which  is  continuous  with  OA  and  lies 
above  OC,  the  vapour  pressure  curve  for  ice.  These  results 
illustrate  two  important  rules  :  (i)  there  is  no  abrupt  change 
in  the  properties  of  a  liquid  at  its  freezing-point  when  the 
solid  phase  does  not  separate ;  (2)  the  vapour  pressure  of  an 
unstable  phase  is  greater  than  that  of  the  stable  phase  at  the 
same  temperature.  The  last  result  may  be  anticipated,  since  it 
is  then  evident  how  an  unstable  phase  may  change  to  a  stable 
phase  by  distillation. 

The  phase  rule  may  now  be  enunciated  as  follows :  If  P 
represents  the  number  of  phases  in  a  system,  C  the  number  oj 
components  and  F  the  number  of  degrees  of  freedom,  the  rela- 
tion between  the  number  of  phases,  components  and  degrees  of 
freedom  is  represented  by  the  equation  C  —  P  +  2  =  F. 

The  meaning  of  the  terms  "  component "  and  "  degree  of 
freedom  "  will  become  clear  as  we  proceed.  The  former  has 
already  been  defined  as  the  smallest  number  of  independent 
variables  of  which  the  system  under  consideration  can  be  built 


182        OUTLINES  OF  PHYSICAL  CHEMISTRY 

up.  Thus  in  the  case  of  water,  considered  above,  there  is  only 
one  component,  and  the  system  calcium  carbonate -calcium 
oxide-carbon  dioxide  can  be  built  up  from  two  components, 
say  calcium  oxide  and  carbon  dioxide.  Particular  instances  of 
the  application  of  the  phase  rule  will  now  be  given. 

If  the  number  of  phases  exceeds  the  number  of  components  by 
2,  the  system  has  no  degrees  of  freedom  (F  =  o),  and  is  said  to 
be  non-variant.  An  illustration  of  this  is  the  triple  point  O 
in  the  diagram  for  water  (p.  180),  where  there  are  three  phases 
(liquid  water,  ice  and  water  vapour)  and  one  component  (water). 
If  one  of  the  variables,  the  temperature  or  the  pressure,  is 
altered  and  kept  at  the  new  value,  one  of  the  phases  disappears  ; 
in  other  words,  the  system  has  no  degrees  of  freedom. 

If  the  number  of  phases  exceeds  the  number  of  components  by 
one  F  =  i,  and  the  system  is  said  to  be  univariant.  As  an  illus- 
tration, we  take  the  case  of  water  vapour,  where  there  are  two 
phases  and  one  component,  say  any  point  on  the  line  OA.  In 
this  case  the  temperature  may  be  altered  within  limits  without 
altering  the  number  of  phases.  If  the  temperature  is  raised,  the 
pressure  will  increase  correspondingly,  and  the  system  will  thus 
adjust  itself  to  another  point  on  the  curve  OA.  Similarly,  the 
pressure  may  be  altered  within  limits,  the  system  will  re-attain  to 
equilibrium  by  a  change  of  temperature  at  the  new  pressure. 
If,  however,  the  temperature  be  kept  at  an  arbitrary  value  and 
the  pressure  is  then  changed,  one  of  the  phases  will  disappear  ; 
the  system  has  therefore  one,  and  only  one,  degree  of  freedom. 

If  the  number  of  phases  is  equal  to  the  number  of  components, 
the  system  has  two  degrees  of  freedom,  and  is  said  to  be  divariant. 
The  areas  in  the  diagram  (Fig.  22)  are  examples  of  this  case — 
there  is  one  phase  (vapour,  liquid  or  solid)  and  one  component. 
If,  for  instance,  we  consider  the  vapour  phase,  the  temperature 
may  be  fixed  at  any  desired  point  within  the  triangle  AOC,  and 
the  pressure  may  still  be  altered  within  limits  along  a  line 
parallel  to  the  pressure  axis  without  alteration  in  the  number 
of  phases,  as  long  as  the  curves  OA  and  OC  are  not  reached. 


HETEROGENEOUS  EQUILIBRIUM  183 

If  the  number  of  phases  is  less  than  the  number  of  com- 
ponents by  one,  the  system  is  Invariant,  and  so  on.  This 
particular  instance  cannot  occur  in  the  case  of  water,  but  does 
so  in  a  four-phase  system,  as  described  in  the  next  section. 

Equilibrium  between  Four  Phases  of  the  same  Sub- 
stance. Sulphur — The  diagram  for  water  represents  the  equi- 
librium between  three  phases  of  the  same  substance.  We  are 
now  concerned  with  sulphur,  which  is  somewhat  more  compli- 
cated inasmuch  as  there  are  two  solid  phases,  monoclinic  and 
rhombic  sulphur,  in  addition  to  the  usual  liquid  and  vapour 
phases. 

Rhombic  sulphur  is  stable  at  the  ordinary  temperature,  and 
on  heating  rapidly  melts  at  115°.  On  being  kept  for  some  time 
in  the  neighbourhood  of  100°,  however,  it  changes  completely 
to  monoclinic  sulphur,  which  melts  at  120°.  Monoclinic  sulphur 
can  be  kept  for  an  indefinite  time  at  100°  without  changing  to 
rhombic ;  it  is  therefore  the  stable  phase  under  these  conditions. 
Thus,  just  as  water  is  the  stable  phase  above  o°  and  ice  is  stable 
below  o°,  there  is  a  temperature  above  which  monoclinic  sulphur 
is  stable,  below  which  rhombic  sulphur  is  stable,  and  at  which 
the  two  forms  are  in  equilibrium  with  their  vapour.  This  tem- 
perature is  termed  the  transition  point,  and  occurs  at  95*6°. 
The  change  of  one  form  into  another  is  under  ordinary  condi- 
tions comparatively  slow,  and  it  is  therefore  possible  to  determine 
the  vapour  pressure  of  rhombic  sulphur  up  to  its  melting-point, 
and  that  of  monoclinic  sulphur  below  its  transition  point. 
Although  the  vapour  pressure  of  solid  sulphur  is  comparatively 
small,  it  has  been  measured  directly  down  to  50°. 

The  complete  equilibrium  diagram,  which  includes  the  fixed 
points  just  mentioned,  is  represented  in  Fig.  23.  O  is  the  point 
at  which  rhombic  and  monoclinic  sulphur  are  in  equilibrium 
with  sulphur  vapour,  and  is  consequently  a  triple  point,  analogous 
to  that  for  water ;  OB  is  the  vapour-pressure  curve  of  rhombic 
sulphur,  and  OA  that  of  monoclinic  sulphur.  OA',  which  is 
continuous  with  OA,  is  the  vapour-pressure  curve  of  monoclinic 


1 84        OUTLINES  OF  PHYSICAL  CHEMISTRY 

sulphur  in  the  unstable  or  metastable  condition  ;  OB'  similarly 
represents  the  vapour-pressure  curve  of  rhombic  sulphur  in  the 
unstable  condition,  and  B'  its  melting-point.  It  will  be  observed 
that  in  both  cases  the  metastable  phase  has  the  higher  vapour 
pressure  (p.  181).  The  line  OC  represents  the  effect  of  pressure 
on  the  transition  point  O  and  is  therefore  termed  a  transition 
curve ;  since,  contrary  to  the  behaviour  of  water,  pressure  raises 
the  transition  point,  the  line  is  inclined  away  from  the  pressure 


(131e,400atmos.) 


Vapour 


Temperature— $> 
FIG.  23. 

axis.  Similarly,  the  curve  AC  represents  the  effect  of  pressure 
on  the  melting-point  of  monoclinic  sulphur,  and  as  it  is  less 
inclined  away  from  the  temperature  axis  than  OC,  the  two  lines 
meet  at  C  at  131°  under  a  pressure  of  400  atmospheres.  The 
curve  AD  is  the  vapour-pressure  curve  of  liquid  sulphur  above 
120°,  where  the  liquid  is  stable,  and  AB',  continuous  with  DA, 
is  the  vapour-pressure  curve  of  metastable  liquid  sulphur.  As 
already  indicated,  B'  represents  the  melting-point  of  metastable 


HETEROGENEOUS  EQUILIBRIUM  185 

rhombic  sulphur ;  in  other  words,  it  is  a  metastable  triple  point 
at  which  rhombic  and  liquid  sulphur,  both  in  the  metastable 
condition,  are  in  equilibrium  with  sulphur  vapour.  OB',  as 
already  indicated,  represents  the  vapour-pressure  curve  of  meta- 
stable rhombic  sulphur,  and  the  diagram  is  completed,  both  for 
stable  and  metastable  phases,  by  B'C,  which  represents  the  effect 
of  pressure  on  the  melting-point  of  rhombic  sulphur.  Mono- 
clinic  sulphur  does  not  exist  above  the  point  C;  when  fused 
sulphur  solidifies  at  a  pressure  greater  than  400  atmospheres, 
the  rhombic  form  separates,  whilst,  as  is  well  known,  the 
monoclinic  form  first  appears  on  solidification  under  ordinary 
pressure.  The  areas,  as  before,  represent  each  a  single  phase, 
as  shown  in  the  diagram.  Monoclinic  sulphur  is  of  particular 
interest,  because  it  can  only  exist  in  the  stable  form  within 
certain  narrow  limits  of  temperature  and  pressure,  represented 
in  the  diagram  by  OAC. 

The  phase  rule  is  chiefly  of  importance  in  indicating  what  are 
the  possible  equilibrium  conditions  in  a  heterogeneous  system, 
and  in  checking  the  experimental  results.  To  illustrate  this,  we 
will  use  it  to  find  out  what  are  the  possible  non-variant  systems 
in  the  case  of  sulphur,  just  considered.  From  the  formula 
C  —  P  +  2  =  F,  since  C  =  i,  P  must  be  three  in  order  that 
F  may  be  zero ;  in  other  words,  the  system  will  be  non-variant 
when  three  phases  are  present.  As  any  three  of  the  four  phases 
may  theoretically  be  in  equilibrium,  there  must  be  four  triple 
points,  with  the  following  phases  : — 

(a)  Rhombic  and  monoclinic  sulphur  and  vapour  (the  point  O). 

(b)  Rhombic  and  monoclinic  sulphur  and  liquid  (the  point  C). 

(c)  Rhombic  sulphur,  liquid  and  vapour  (the  point  B'). 

(d)  Monoclinic  sulphur,  liquid  and  vapour  (the  point  A). 
The  phase  rule  gives  no  information,  however,  as  to  whether 
the  triple  points  indicated  can  actually  be  observed.     In  this 
particular  case  they  are  all  attainable,  as  the  diagram  shows, 
but  only  because  the   change   from   rhombic   to   monoclinic 
sulphur  above  the  triple  point  is  comparatively  slow.     If  it 


1 86       OUTLINES  OF  PHYSICAL  CHEMISTRY 


happened  to  be   rapid,   the  point  B'  could  not  be  actually 
observed. 
Systems  of  Two  Components.     Salt  and  Water — The 

equilibrium  conditions  are  somewhat  more  complicated  on 
passing  from  systems  of  one  component  to  those  of  two  com- 
ponents, such  as  a  salt  and  water.  For  simplicity,  the  equi- 
librium between  potassium  iodide  and  water  will  be  considered, 
as  the  salt  does  not  form  hydrates  with  water  under  the  con- 
ditions of  the  experiment.  There  will  therefore  be  only  four 

phases,  solid  salt,  solu- 
tion, ice  and  vapour. 
There  are  three  degrees 

3oo  \-  u          :X  /  of  freedom,  as,  in  ad- 

dition to  the  tempera- 
ture and  pressure,  the 
concentration  of  the 
solution  may  now  be 
varied. 

The    equilibrium    in 

_soo  \-  "  this    system   is    repre- 

sented in  Fig.  24,  the 
ordinates  representing 
temperatures  and  the 
abscissae  concentra- 
tions. At  o°  (A  in  the  diagram)  ice  is  in  equilibrium  with 
water  and  vapour,  as  has  already  been  shown.  If,  now,  a 
little  potassium  iodide  is  added  to  the  water,  the  freezing-point 
is  lowered,  in  other  words,  the  temperature  at  which  ice  and 
water  are  in  equilibrium  is  lowered  by  the  addition  of  a  salt, 
and  the  greater  the  proportion  of  salt  present,  the  lower  is 
the  temperature  of  equilibrium.  This  is  represented  on  the 
curve  AO,  which  is  the  curve  along  which  ice,  solution  and 
vapour  are  in  equilibrium.  On  continued  addition  of  potassium 
iodide,  however,  a  point  must  be  reached  at  which  the  solution 
is  saturated  with  the  salt,  and  on  further  addition  of  potassium 


Grams  Kl    in  100  grams  solution 


10     20    30     40     50     60     70     80     90 
FIG.  24. 


HETEROGENEOUS  EQUILIBRIUM  187 

iodide,  the  latter  must  remain  in  the  solid  form  in  contact  with 
ice  and  the  solution.  It  is  clear  that,  since  the  progressive 
lowering  of  the  freezing-point  depends  upon  the  continuous 
increase  in  the  concentration  of  the  solution,  the  temperature 
corresponding  with  the  point  O  must  represent  the  lowest 
temperature  attainable  in  this  way  under  stable  conditions. 

To  complete  the  diagram,  it  is  further  necessary  to  determine 
the  equilibrium  curve  for  the  solid  salt,  the  solution  and 
vapour.  Looked  at  in  another  way,  this  will  be  the  solubility 
curve  of  potassium  iodide,  which  is  represented  by  the  curve 
OB.  This  curve  is  only  slightly  inclined  away  from  the  tempera- 
ture axis,  corresponding  with  the  fact  that  the  solubility  of 
potassium  iodide  only  increases  slowly  with  rise  of  temperature. 
The  point  O,  which  is  the  lowest  temperature  attainable  with 
two  components,  is  known  as  a  eutectic  point ;  in  the  special 
case  when  the  two  components  are  a  salt  and  water,  it  is  termed 
a  cryohydric  point. 

The  meaning  of  the  diagram  will  be  clearer  if  we  consider 
what  occurs  when  solutions  of  varying  concentration  are  pro- 
gressively cooled.  If,  for  example,  we  commence  with  a  weak 
salt  solution  above  its  freezing-point  (x  in  the  diagram)  and 
continuously  withdraw  heat,  the  temperature  will  fall  (along  xy) 
till  the  line  OA  is  reached ;  ice  will  then  separate,  and  as  the 
cooling  is  continued  the  solution  will  become  more  con- 
centrated and  the  composition  will  alter  along  the  line  AO 
until  O  is  reached ;  salt  then  separates  as  well  as  ice,  and  the 
solution  will  solidify  completely  at  constant  temperature,  that 
of  the  point  O.  Similarly,  if  we  start  with  a  concentrated 
salt  solution  and  lower  the  temperature  until  it  reaches  the 
curve  OB,  salt  will  separate  and  the  composition  will  alter 
along  the  curve  BO  until  it  reaches  the  point  O,  when  the 
mixture  solidifies  as  a  whole.  Finally,  if  a  mixture  corre- 
sponding with  the  composition  of  the  cryohydric  mixture  is 
cooled,  the  line  parallel  to  xy  representing  the  fall  of  tem- 
perature will  meet  the  curve  first  at  the  point  O,  and  the 


1 88       OUTLINES  OF  PHYSICAL  CHEMISTRY 

mixture  will  solidify  at  constant  temperature.  At  the  cryohydric 
temperature,  the  composition  of  the  solid  salt  which  separates  is 
necessarily  the  same  as  that  of  the  solution.  Guthrie,1  who  was 
the  first  to  investigate  these  phenomena  systematically,  was  of 
opinion  that  these  mixtures  of  constant  composition  were  definite 
hydrates,  which  were  therefore  termed  cryohydrates.  At  first 
sight  there  seems  much  to  be  said  for  this  view,  as  the  separa- 
tion takes  place  at  constant  temperature,  independent  of  the 
initial  concentration,  and  the  mixtures  are  crystalline.  For  the 
following  reasons,  however,  it  is  now  accepted  that  the  cryo- 
hydrates  are  not  chemical  compounds :  (a)  the  properties  of 
the  mixture  (heat  of  solution,  etc.)  are  the  mean  of  the  pro- 
perties of  the  constituents,  which  is  seldom  the  case  for  a  chemical 
compound;  (b}  the  components  are  not  usually  present  in 
simple  molar  proportions;  and  (c)  the  heterogeneous  character 
of  the  mixture  can  be  recognised  by  microscopic  examination. 
The  magnitude  of  the  cryohydric  temperature  is  of  course  con- 
ditioned by  the  effect  of  the  salt  in  lowering  the  freezing-point 
of  the  solvent,  and  by  its  solubility  at  low  temperatures.  The 
eutectic  temperatures  of  solutions  of  sodium  and  ammonium 
chlorides  are  —  22°  and  —  17°  respectively,  that  of  a  solution  of 
calcium  chloride  -  37°. 

The  application  of  the  phase  rule  to  this  system  will  be 
readily  understood  from  what  has  been  said  above.  When  there 
are  four  phases,  ice,  salt,  solution  and  vapour,  and  two  com- 
ponents, we  find,  by  substituting  in  the  formula  C-P+2=F, 
that  F  =  o,  that  is,  the  four  phases  can  only  be  in  equilibrium 
at  a  single  point,  the  point  O  in  the  diagram.  When  there  are 
three  phases,  there  is  one  degree  of  freedom,  and  the  equi- 
librium is  represented  by  a  line  (OA  and  OB  in  the  diagram). 
If,  for  example,  the  condition  of  affairs  is  that  represented  by  a 
point  on  the  line  OA,  and  the  concentration  of  the  solution  is 
increased  and  kept  at  the  new  value  (by  further  addition  of 
salt  when  necessary)  ice  will  dissolve,  and  the  temperature  will 
fall  till  it  corresponds  with  that  at  which  ice  is  in  equilibrium 
lPhil.  Mag.,  1884,  [5],  17,  462. 


HETEROGENEOUS  EQUILIBRIUM  189 

with  the  more  concentrated  solution  and  vapour.  If,  then,  while 
the  concentration  is  still  kept  at  the  above  value,  the  tempera- 
ture is  altered  and  kept  at  the  new  value,  one  of  the  phases  will 
disappear.  The  system  is  therefore  univariant.  If,  instead  of 
the  concentration,  one  of  the  other  variables  is  changed,  corre- 
sponding changes  in  the  remaining  two  variables  take  place, 
and  the  system  adjusts  itself  till  the  three  phases  are  again  in 
equilibrium. 

If  there  are  only  two  phases,  for  example,  solution  and  vapour, 
the  phase  rule  indicates  that  the  system  is  bivariant,  and  it  can 
readily  be  shown,  by  reasoning  analogous  to  the  above,  that 
such  is  the  case. 

Freezing  Mixtures — The  use  of  mixtures  of  ice  and  salt 
as  "  freezing  mixtures  "  for  obtaining  constant  low  temperatures, 
depends  upon  the  principles  just  discussed.  Suppose,  for 
example,  we  begin  with  a  fairly  intimate  mixture  of  ice  and 
salt  and  a  little  water.  When  a  little  of  the  salt  dissolves,  the 
solution  is  no  longer  in  equilibrium  with  ice.  It  will  strive 
towards  equilibrium  by  some  more  ice  dissolving  to  dilute  the 
solution,  the  latter,  being  now  more  unsaturated  with  regard 
to  the  salt,  will  dissolve  more  of  it,  more  ice  will  go  into 
solution  and  so  on.  As  a  consequence  of  these  changes,  heat 
must  be  absorbed  in  changing  ice  to  water  (latent  heat  of  fusion 
of  ice),  and  in  connection  with  the  heat  of  solution  of  the  salt 
if,  as  is  usually  the  case,  the  heat  of  solution  is  negative.  The 
temperature,  therefore,  falls  till  the  cryohydric  point  is  reached, 
and  then  remains  constant,  since  it  is  under  these  conditions 
that  ice,  salt,  solution  and  vapour  are  in  equilibrium.  As 
the  temperature  of  a  cryohydric  mixture  is  so  much  below 
atmospheric  temperature,  heat  will  continually  be  absorbed  from 
the  surroundings,  but  as  long  as  both  ice  and  solid  salt  are 
present,  the  heat  will  be  used  up  in  bringing  about  the  change 
of  state,  and  the  temperature  will  remain  constant.  When, 
however,  either  ice  or  salt  is  used  up,  the  temperature  must 
necessarily  begin  to  rise. 


1 9o       OUTLINES  OF  PHYSICAL  CHEMISTRY 

Systems  of  Two  Components.  General — The  particular 
case  of  a  two-component  or  binary  system  already  considered — 
potassium  iodide  and  water — is  very  simple,  for  two  reasons : 
(i)  the  solid  phases  separate  pure  from  the  fused  mass,  in  other 
words,  the  phases  are  not  miscible  in  the  solid  state ;  (2)  the 
components  do  not  enter  into  chemical  combination.  Com- 
plications occur  when  chemical  compounds  are  formed,  and 
when  the  solid  phases  separate  as  mixed  crystals  (p.  95)  con- 
taining the  two  components  in  varying  proportions.  We  will 
consider  three  comparatively  simple  cases  of  equilibrium  in  binary 
systems,  the  components  being  in  all  cases  completely  miscible 
in  the  fused  state  : — 

(a)  The  components  do  not  enter  into  chemical  combination, 
and  are  not  miscible  in  the  solid  state. 

(b)  The  components  do  not  enter  into  chemical  combination, 
but  are  completely  miscible  in  the  solid  state. 

(c)  The  components  form  one  chemical  compound,  but  are 
not  miscible  with  each  other  or  with   the   compound  in  the 
solid  state. 

Case  (a).  One  example  of  this  case  is  potassium  iodide  and 
water  which  has  just  been  discussed.  Another,  which  will  be 
briefly  considered,  is  the  equilibrium  between  the  metals  zinc 
and  cadmium.1  To  determine  the  equilibrium  curves,  mixtures 
of  these  metals  in  varying  proportions  are  heated  above  the 
melting-point,  and  then  allowed  to  cool  slowly,  the  rate  of 
cooling  being  observed  with  a  thermocouple,  one  junction  of 
which  is  placed  in  the  mixture  and  the  other  kept  at  constant 
temperature.  If  the  thermocouple  is  connected  to  a  mirror 
galvanometer,  the  rate  of  cooling  can  be  followed  by  the  move- 
ment of  a  spot  of  light.  It  will  be  observed  that  at  two  points 
there  are  halts  in  the  rate  of  cooling — so-called  "  breaks  " — 
the  first  point  varies  with  the  composition  of  the  mixture,  whilst 
the  second  is  practically  constant  at  270°.  The  curve  obtained 
by  plotting  the  temperatures  of  the  first  break  against  the 

1  Hinrichs,  Zeitsch.  anorg.  Chem.,  1907,  55,  415. 


HETEROGENEOUS  EQUILIBRIUM 


191 


composition  of  the  mixture  is  represented  in  Fig.  25.  The 
analogy  of  the  diagram  with  that  for  potassium  iodide  and  water 
will  be  evident,  as  is  its  interpretation.  The  point  A  represents 
the  freezing-point  of  zinc,  B  that  of  cadmium,  the  curve  AC 
represents  the  effect  of  the  gradual  addition  of  cadmium  upon 
the  freezing-point  of  zinc,  and  BC  the  effect  of  zinc  in  lowering 


B  A 


X  o  °/0  Cd  Z 

Equilibrium  Diagram  for  Zinc  and  Cadmium 

FIG.  25. 


ioo  °/o  Cd 


the  freezing-point  of  cadmium,  C  is  the  eutectic  point  at  which 
solid  zinc  and  cadmium  are  in  equilibrium  with  the  fused  mass. 
Consider  first  a  fused  mixture  rich  in  zinc.  As  the  temperature 
falls,  a  point  is  ultimately  reached  at  which  pure  zinc  begins  to 
separate,  and  as  the  change  from  liquid  to  solid  is,  as  usual, 
attended  with  liberation  of  heat,  the  temperature  will  remain 
practically  steady  for  a  short  time — this  represents  the  first 
break  on  cooling.  As  zinc  continues  to  separate,  the  composi- 
tion of  the  mixture  moves  along  the  curve  AC,  at  C  the  solution 


192        OUTLINES  OF  PHYSICAL  CHEMISTRY 

is  also  saturated  with  regard  to  cadmium,  and  tnerefore  at  the 
temperature  represented  by  C,  both  zinc  and  cadmium  separate 
in  a  mixture  of  the  same  composition  as  the  fused  mass.  This, 
as  already  mentioned,  is  the  eutectic  point,  and  as  the  mixture 
at  that  point  behaves  like  a  single  substance,  the  temperature 
remains  constant  till  the  whole  mass  has  solidified.  This  is 
the  second  break  observed  when  the  mixture  cools. 

If,  on  the  other  hand,  we  commence  with  a  mixture  rich  in 
cadmium,  the  latter  separates  along  the  curve  BC  till  the  point 
C  is  reached,  and  then  the  mixture  solidifies  as  a  whole.  Finally, 
if  a  mixture  is  taken,  the  composition  of  which  is  that  of  the 
eutectic  mixture,  there  is  only  one  break  in  the  cooling  curve, 
at  the  eutectic  point.  The  composition  of  the  eutectic  mixture 
is  represented  by  the  point  Z  on  the  axis  of  composition  XY, 
and  corresponds  with  17*4  per  cent,  of  zinc  and  82-6  per  cent,  of 
cadmium  by  weight. 

Case  (<£).  No  chemical  compound.  Separation  of  mixed 
crystals.  A  good  example  of  this  case  is  the  system 
palladium-gold,1  the  equilibrium  diagram  for  which  is  repre- 
sented in  Fig.  26.  Here  there  is  only  one  break  in  the  cooling 
curve,  and  the  temperature  of  the  break  gradually  falls  from  B, 
the  melting-point  of  the  pure  metal  with  the  higher  melting- 
point  (in  this  case  gold),  to  A,  the  melting-point  of  palladium. 
In  this  case,  when  the  fused  mass  is  allowed  to  cool,  crystals 
containing  both  metals  in  varying  proportions  separate,  and 
therefore  the  ordinary  rule  with  regard  to  the  lowering  of 
melting-point  of  one  substance  by  the  addition  of  another  does 
not  apply,  and  there  is  no  eutectic  point  (p.  187).  Gold  and 
palladium  are  miscible  in  all  proportions  in  the  solid  state,  but 
in  many  cases  the  miscibility  is  limited.  As  the  composition 
of  the  crystals  and  the  solution  does  not  remain  the  same 
during  solidification,  there  is  in  general  an  interval  of  tempera- 
ture, termed  the  crystallisation  interval,  between  the  beginning 
and  end  of  crystallisation. 

1  Ruer,  Zeitsch.  anorg.  Chem.,  1906,  51,  391. 


HETEROGENEOUS  EQUILIBRIUM 


'93 


XO°/0Au 

Composition 
Equilibrium  Diagram  for  Palladium  and  Gold 

FIG.  26. 


0%T1  Z  (Hg2  Tl). 

Composition 
Equilibrium  Diagram  for  Mercury  and  Thallium 

FIG.  27. 


100%  Tl 


194        OUTLINES  OF  PHYSICAL  CHEMISTRY 

Case  (c].  One  chemical  compound.  No  miscibility  in  solia 
form.  A  typical  freezing-point  curve  for  a  system  of  this 
type  is  given  in  Fig.  27,  representing  thallium- mercury  amal- 
gams. It  will  be  observed  that  there  is  a  maximum  on  the 
curve,  corresponding  with  the  composition  of  a  compound 
Hg2Tl,  containing  two  equivalents  of  mercury  to  one  of 
thallium.  This  compound  melts  at  a  definite  temperature, 
and  it  is  evident  from  the  curve  that  the  melting-point  is 
lowered  both  by  the  addition  of  mercury  (along  CB)  and  of 
thallium  (along  CD).  From  this  it  is  clear  that  the  components 
of  a  chemical  compound  lower  the  freezing-point  of  the  compound 
just  as  foreign  substances  do.  The  remainder  of  the  curve  will 
readily  be  understood  from  the  previous  paragraphs.  A  repre- 
sents the  freezing-point  of  mercury,  AB  the  lowering  of  the 
freezing-point  of  mercury  by  the  progressive  addition  of  the 
compound  Hg2Tl,  E  the  melting-point  of  thallium,  and  ED 
the  effect  on  the  melting-point  of  thallium  produced  by  gradu- 
ally increasing  amounts  of  the  same  compound.  The  points  B 
and  D  are  eutectic  points,  the  eutectic  mixtures  containing 
mercury  and  Hg2Tl,  and  Hg2Tl  and  thallium,  respectively. 

The  occurrence  of  a  maximum  on  the  freezing-point  curve  is 
usually  an  indication  of  chemical  combination,  but,  on  the  other 
hand,  chemical  compounds  are  sometimes  present,  although 
there  are  no  maxima  on  the  curve.  This  occurs  more  par- 
ticularly when  the  chemical  compound  decomposes  before  its 
melting-point  is  reached. 

The  systematic  investigation  of  the  freezing-point  curve  of  a 
binary  mixture  is  one  of  the  best  methods  for  detecting  chemical 
compounds  and  establishing  theii  formulae.  This  can  be  illus- 
trated by  the  equilibrium  curve  of  ferric  chloride  and  water, 
which  is  of  great  historical  interest,  inasmuch  as,  in  the  course 
of  the  investigation  of  this  system  by  Roozeboom,  many  of  the 
points  we  have  been  discussing  were  elucidated. 

The  Hydrates  of  Ferric  Chloride— The  freezing-point 
curve  of  this  system  is  represented  in  Fig.  28,  and  will  be 


HETEROGENEOUS  EQUILIBRIUM  195 

readily  understood  by  comparison  with  the  previous  diagrams, 
more  particularly  Fig.  27.  For  convenience,  the  concentrations 
in  this  case  are  expressed  as  the  ratio  of  the  number  of  mols 
of  ferric  chloride  present  to  100  mols  of  water. 

In  interpreting  the  curve,  we  commence  at  the  left-hand  side 
of  the  diagram.     A  represents  the  freezing-point  of  water,  and 


O       5      10      15      20    25   3o  35         X 

Mols.  Fe;iCl8  to  100  mols.  H2O 
FlG.    28. 

AB  the  lowering  of  freezing-point  produced  by  the  progressive 
addition  of  ferric  chloride.  At  the  point  B,  -  55°,  the  solution 
is  saturated  with  regard  to  ferric  chloride,  and  B  is  therefore  the 
eutectic  point,  at  which  ice,  solution,  a  hydrate  of  ferric  chloride 
(Fe2Cl6,  i2H2O)  and  vapour  are  in  equilibrium.  On  adding 
more  ferric  chloride,  the  ice  phase  will  disappear,  and  equilibrium 
will  be  attained  at  a  point  on  the  curve  BC,  at  which  the 


196        OUTLINES  OF  PHYSICAL  CHEMISTRY 

dodecahydrate,  Fe2Cl6,  i2H2O,  is  in  equilibrium  with  solution 
and  vapour.  The  curve  BC  may  therefore  be  regarded  as  the 
solubility  curve  of  the  dodecahydrate,  and  corresponds  exactly 
with  the  curve  OB  (Fig.  24).  On  continued  addition  of  ferric 
chloride,  the  equilibrium  temperature  continues  to  rise  up  to  the 
point  C  at  37°,  at  which  point  the  composition  of  the  mixture 
corresponds  with  that  of  the  dodecahydrate.  Further  addition  of 
ferric  chloride  lowers  the  temperature  along  the  line  CD,  so  that 
C  is  a  maximum  on  the  curve.  At  this  point,  the  solid  dodeca- 
hydrate is  in  equilibrium  with  a  liquid  of  the  same  composition  ; 
in  other  words,  C  is  the  melting-point  of  the  compound 
Fe2Cl6,  i2H2O,  just  as  the  point  C  (Fig.  27)  represents  the 
melting-point  of  Hg2Tl.  On  addition  of  more  ferric  chloride, 
the  melting-point  is  lowered,  as  represented  by  the  section  CD 
of  the  curve.  At  the  point  D,  the  curve  reaches  another 
minimum,  or  eutectic  point,  which  corresponds  with  the  point 
B,  except  that  a  new  hydrate,  Fe2Cl6,  7H2O,  takes  the  place  of 
ice.  On  further  addition  of  ferric  chloride,  another  maximum 
is  reached,  which  represents  the  melting-point  of  the  hepta- 
hydrate.  In  an  exactly  similar  way,  the  other  two  maxima  at 
higher  concentrations  of  ferric  chloride  indicate  the  existence 
of  two  other  hydrates,  Fe2Cl6,  5H2O  and  Fe2Cl6,  4H2O,  in  the 
solid  state.  At  the  last  eutectic  point,  K,  the  four  phases  in 
equilibrium  are  the  tetrahydrate,  anhydrous  ferric  chloride,  solu- 
tion and  vapour,  and  KL  represents  the  effect  of  temperature 
on  the  solubility  of  the  anhydrous  chloride. 

The  application  of  the  phase  rule  to  this  system  should  be 
made  by  the  student.  As  at  the  point  D  (and  the  other  corre- 
sponding points)  the  solubility  curves  of  the  dodecahydrate 
and  heptahydrate  intersect,  D  may  be  termed  the  transition 
point  for  the  two  hydrates.  Since  at  these  points  there  are  four 
phases  in  equilibrium,  they  are  also  termed  quadruple  points. 

In  recent  years,  many  other  systems  have  been  fully  investi- 
gated on  analogous  lines  to  that  indicated  above.  The  chief 
experimental  difficulty  is  to  avoid  supercooling,  a  source  of 


HETEROGENEOUS  EQUILIBRIUM  197 

error  which  is  much  more  troublesome  in  some  systems  than 
in  others. 

Transition  Points — In  the  preceding  sections,  mention  has 
been  made  on  several  occasions  of  transition  points.  When  a 
substance  is  polymorphic  (i.e.,  exists  in  more  than  one  form)  it 
is  often  possible,  as  in  the  case  of  sulphur,  to  find  a  temperature 
— the  so-called  transition  point — at  which  two  forms  are  in 
equilibrium ;  at  higher  temperatures  one  of  the  forms  is  stable, 
at  lower  temperatures  the  other. 

It  has  been  shown  that  at  the  transition  point  the  two 
modifications  have  the  same  vapour  pressure,  but  at  other 
temperatures  the  metastable  form  has  the  higher  vapour 
pressure.  By  similar  reasoning  it  can  be  shown  that  the 
metastable  phase  has  the  higher  solubility  and  the  lower  melt- 
ing-point. 

It  may  happen,  however,  as  in  the  case  of  benzophenone, 
that  the  modification  stable  at  low  temperatures  melts  before 
the  transition  point  is  reached.  It  is  evident  that  in  this  case 
the  transition  can  only  take  place  in  one  direction,  from  the 
modification  the  existence  of  which  is  favoured  by  high  tem- 
perature to  that  stable  at  low  temperatures.  Substances  such 
as  sulphur,  for  which  there  is  a  reversible  transition,  are  termed 
enantiotropic,  substances  for  which  the  transition  is  only  in  one 
direction  are  termed  monotropic. 

It  may  be  asked  how  it  is  possible  to  obtain  the  metastable 
form  of  benzophenone,  as  it  is  necessarily  unstable  under  all 
conditions.  The  explanation  is  that  when  a  fused  polymorphic 
substance  is  allowed  to  solidify,  it  is  generally  the  most  unstable 
form  which  separates  first  (e.g.,  sulphur). 

Similarly,  the  transition  point  of  two  hydrates  is  that  tempera- 
ture at  which  they  are  in  equilibrium,  and  at  which  they  have 
the  same  solubility. 

Practical  Illustrations.  Distribution  of  a  solute  between 
two  immiscible  solvents — To  a  nearly  saturated  aqueous  solu- 
tion of  succinic  acid  (say  100  c.c.)  in  a  stoppered  bottle  an 


198       OUTLINES  OF  PHYSICAL  CHEMISTRY 

approximately  equal  volume  of  ether  is  added,  and  the  bottle 
kept  at  room  temperature  for  half  an  hour,  shaking  it  at  intervals. 
When  the  separation  into  two  layers  is  complete,  part  of  the 
ethereal  layer  is  pipetted  off  and  titrated  with  barium  hydroxide, 
and  the  same  is  done  with  the  aqueous  layer.  Less  concentrated 
solutions  of  succinic  acid  are  then  used,  and  the  concentrations 
in  the  ethereal  and  aqueous  layers  determined  as  before.  The 
value  of  the  distribution  constant  Cj/C2  is  then  calculated  from 
the  results,  and  should  be  constant,  as  the  molecular  weight  is 
the  same  in  the  two  solvents  (p.  178). 

In  a  similar  way  the  distribution  of  benzoic  acid  between 
water  and  benzene  may  be  investigated.  In  this  case,  as  ben- 
zoic acid  is  unimolecular  in  water  and  bimolecular  in  benzene 
(p.  179),  the  ratio  CJ  \/C2,  where  Cj  represents  the  concentration 
in  the  aqueous  layer,  C2  the  concentration  in  the  benzene  layer, 
should  be  approximately  constant. 

Determination  of  transition  points — Transition  temperatures, 
such  as  that  above  which  rhombic  sulphur  is  unstable  and 
monoclinic  sulphur  stable,  can  be  determined  in  various  ways, 
which  depend  in  principle  on  the  difference  in  properties  of 
the  two  phases.  The  dilatometer  method  is  largely  used ;  it 
depends  on  the  fact  that  there  is  a  more  or  less  sudden  change 
of  volume  when  the  transition  takes  place.  Into  a  fairly  wide 
glass  tube,  provided  with  a  capillary  tube  and  scale  at  the 
upper  end  and  open  at  the  lower  end,  is  placed  a  mixture  of 
the  two  modifications,  e.g.,  monoclinic  and  rhombic  sulphur, 
the  lower  end  is  then  sealed  up,  and  the  vessel  filled  to  the 
lower  end  of  the  scale  with  an  indifferent  liquid  such  as  oil. 
The  dilatometer  is  then  placed  in  a  bath  the  temperature  of 
which  is  gradually  raised,  and  readings  made  of  the  level  of  the 
liquid  in  the  dilatometer.  The  rate  of  change  of  level  will  be 
more  or  less  steady  till  the  neighbourhood  of  the  transition 
point  is  reached,  when  a  relatively  rapid  change  of  level  will  be 
observed.  The  chief  drawback  to  the  method  is  that  the 
change  seldom  takes  place  rapidly  when  the  transition  point  is 


HETEROGENEOUS  EQUILIBRIUM  199 

reached.     To  facilitate  the  change  as  far  as  possible,  some  of 
the  second  phase  should  always  be  present,  (p.  55). 

By  solubility  or  vapour-pressure  measurements — The  fact 
that  the  two  phases  have  the  same  solubility  at  the  transition 
point  may  be  employed  to  determine  the  latter.  To  determine 
the  transition  point  in  the  system  Na2SO4,io  H2O  ^±  Na2SO4  + 
10  H2O,  it  is  only  necessary  to  measure  the  solubility  of  the 
anhydrous  salt  and  of  the  decahydrate  in  the  neighbourhood 
of  the  transition  point,  and  the  point  at  which  the  solubility 
curves  intersect  will  be  the  required  point. 

Measurements  of  vapour  pressure  may  be  employed  in  a 
similar  way.  Thus  Ramsay  and  Young  determined  the  vapour 
pressures  of  solid  and  liquid  bromine  respectively  and  found 
that  the  curves  intersected  at  -  7°,  which  is  therefore  the 
transition  temperature  for  solid  and  liquid  bromine ;  in  other 
words,  the  melting-point  of  bromine. 


CHAPTER  IX 
VELOCITY  OF  REACTION.     CATALYSIS 

General — In  inorganic  chemistry,  the  question  as  to  the 
rate  of  a  chemical  change  does  not  often  arise,  because  in 
general  the  reactions  are  so  rapid  that  it  is  impossible  to  measure 
the  speed.  The  neutralization  of  an  acid  by  a  base,  for  instance, 
as  shown  by  the  change  of  colour  of  the  indicator,  is  practically 
instantaneous.  However,  some  instances  of  slow  inorganic  re- 
actions in  homogeneous  systems  are  known.  The  rate  of  com- 
bination of  sulphur  dioxide  and  oxygen  to  form  sulphur  trioxide 
is  very  slow  under  ordinary  conditions,  and  the  mixture  of  gases 
has  to  be  heated  in  contact  with  platinum  as  an  accelerating 
agent  in  order  to  obtain  a  good  yield  of  trioxide.  In  organic 
chemistry,  on  the  other  hand,  slow  chemical  reactions  are  very 
frequently  met  with.  Thus  the  combination  of  an  organic  acid 
and  an  alcohol  to  form  an  ester  is  very  slow  under  ordinary 
conditions,  and  the  mixture  of  acid  and  alcohol,  saturated 
with  hydrogen  chloride,  has  to  be  boiled  for  a  considerable 
time  in  order  to  obtain  a  good  yield  of  ester. 

In  this  chapter,  as  in  the  preceding  one  on  chemical  equili- 
brium, the  law  of  mass-action  is  the  guiding  principle.  It  has 
already  been  pointed  out  (p.  158)  that  the  rate  of  a  chemical 
reaction  at  any  instant  may  be  regarded  as  the  difference  in 
the  speeds  of  the  direct  and  the  reverse  reaction  at  that  instant. 
If  we  consider  a  simple  reversible  reaction,  such  as  ester  forma- 
tion, in  which  a,  bt  c  and  d  are  the  initial  equivalent  concentra- 
tions of  the  reacting  substances,  and  if  x  is  the  amount  of 

200 


VELOCITY  OF  REACTION.     CATALYSIS      201 

ester  formed  in  the  time  /,  the  equation  for  the  reaction  velo- 
city at  that  instant  may  be  written 

*-£  =  k(a  -  x)(b  -  x)  -k&  +  x)(d+X)         .     (i) 

in  which  dx  represents  the  small  increase  in  the  amount  of  x 
during  the  small  interval  of  time,  dt.  This  equation  is  a  direct 
consequence  of  the  application  of  the  law  of  mass  action  to  the 
reaction  in  question. 

It  very  often  happens,  however,  that  the  equilibrium  lies  very 
near  one  side,  which  can  only  mean  that  the  rate  of  the  reverse 
reaction  is  small  in  comparison  with  that  of  the  direct  reaction. 
This  is  clear  from  the  following  considerations.  The  splitting 
up  of  hydrogen  peroxide  into  water  and  oxygen  is  represented 
by  the  equation  H2O2->H2O  +  £O2,  and  the  equilibrium  be- 
tween this  compound  and  its  decomposition  products  by  the 
equation  H2O22H2O  +  -JO2.  Applying  the  law  of  mass  action, 
we  have 


and 

[HA]       _*,_K 

[H20]  [OJ*      k    ' 

N"ow  it  is  an  experimental  fact  that  the  concentration  of  hydrogen 
peroxide  in  equilibrium  with  water  and  oxygen  at  atmospheric 
pressure  is  so  small  that  it  cannot  be  detected  by  analytical 
means.  It  follows,  from  the  above  equation,  that  k^  is  small  in 
comparison  with  k  ;  otherwise  expressed,  the  rate  of  the  con- 
verse reaction,  represented  by  the  lower  arrow,  is  negligible  in 
comparison  with  that  of  the  direct  reaction,  represented  by  the 
upper  arrow. 

The  same  considerations  apply  to  the  more  general  case  re- 
presented by  equation  (i).  If  k^  is  negligible  in  comparison 
with  k,  the  expression  k^(c  +  x)(d  +  x)  in  equation  (i)  is 
negligible  in  comparison  with  the  remainder  of  the  right-hand 
side  of  the  equation,  and  the  latter  therefore  simplifies  to 


202       OUTLINES  OF  PHYSICAL  CHEMISTRY 

dx       ,,  N/i         x 

—  =  k(a-  x)(b  -  x). 

Reactions  of  this  type,  in  which  the  rate  of  the  inverse  reaction 
is  negligible,  are  by  far  the  simplest  from  a  kinetic  standpoint, 
and  will  therefore  be  considered  first. 

Uni molecular  Reaction — The  simplest  type  of  chemical 
reaction  is  that  in  which  only  one  substance  is  undergoing 
change,  and  there  is  practically  no  back  reaction.  Such  a 
reaction,  which  can  be  readily  followed,  is  the  splitting  up  of 
hydrogen  peroxide  to  water  and  oxygen  in  the  presence  of 
colloidal  platinum  or  of  certain  enzymes.  The  reaction,  which 
is  usually  carried  out  in  dilute  aqueous  solution,  may  be  repre- 
sented by  the  equation  H2O2  =  H2O  4-  O,  and  there  is  the 
advantage  that  the  solvent  does  not  appreciably  alter  during 
the  reaction.  As  the  colloidal  platinum  or  the  enzyme  remains 
of  constant  activity  during  the  reaction,  the  course  of  reaction 
is  determined  solely  by  the  peroxide  concentration  (cf.  p.  205). 

The  reaction  in  the  presence  of  haemase  (blood -catalase)  can 
conveniently  be  followed  by  removing  a  portion  of  the  solution 
from  time  to  time,  adding  to  excess  of  sulphuric  acid,  which 
immediately  stops  the  reaction,  and  titrating  with  permanganate 
solution.  Some  of  the  results  obtained  in  this  way  are  repre- 
sented in  the  accompanying  table  : — 

t  (mins.). 
o 

5 
10 

20 

3° 

50  5*0  41*1 

The  numbers  in  the  second  column  represent  the  number  of 
c.c.  of  dilute  permanganate  solution  equivalent  to  25  c.c.  of 
the  reaction  mixture  when  the  times  represented  in  the  first 


a-x 
(c.c.  KMnO4). 

x 
(c.c.  KMnO4). 

k 

46'i 

0 

— 

29-8 
19*6 

9'0 

16-3 
26-5 

°'°435 
0-0438 
0*0429 

12-3 

33'8 

0*0440 

VELOCITY  OF  REACTION.     CATALYSIS      203 

column  have  ekpsed  after  mixing  the  peroxide  and  enzyme, 
and  therefore  represent  the  concentrations  of  peroxide  in  the 
mixture  at  the  times  in  question.  By  subtracting  these  numbers 
from  that  representing  the  initial  concentration  of  the  peroxide, 
46*1  c.c.,  the  amounts  of  peroxide  split  up  at  the  times  /  are 
obtained  ;  these  numbers  are  given  in  the  third  column. 

The  numbers  illustrate  very  clearly  the  falling  off  in  the  rate 
of  the  reaction  as  the  concentration  of  the  peroxide  diminishes. 
Thus  in  the  first  ten  minutes  an  amount  of  peroxide  equivalent 
to  1  6*3  c.c.  of  permanganate  is  split  up,  whilst  in  the  second 
interval  of  ten  minutes  only  26*5  —  16*3  10*2  c.c.  are  de- 
composed. 

According  to  the  law  of  mass  action,  the  rate  of  the  reaction 
at  the  time  t  should  be  proportional  to  the  concentration  of  the 
peroxide,  a  —  x,  at  that  time,  hence 

•£-*(«-*)  ...          (2) 

In  this  form,  however,  the  equation  cannot  be  applied  directly 
to  the  experimental  results,  since  dx,  the  amount  of  change  of 
x  in  the  time  dt,  would  have  to  be  taken  fairly  large  in  order  to 
obtain  accurate  results,  and  during  the  interval  a  —  x  would 
naturally  have  diminished.  Better  results  would  be  obtained 
if  a-x  were  taken  as  the  average  concentration  during  the 
interval  dt  within  which  dx  of  peroxide  is  being  decomposed, 
but  even  this  method  does  not  give  accurate  values  for  k.  The 
difficulty  is  got  over  by  integrating  the  equation  on  principles 
described  in  books  on  higher  mathematics.  In  this  way,  and 
bearing  in  mind  that,  when  /=  o,  x  =  o,  we  obtain  from  equation 
(2)  above 

=  *     ...    (3) 


It  is,  however,  much  more  convenient  to  work  with  ordinary 
logarithms  (to  the  base  10)  than  with  logarithms  to  the  base  e. 
Making  the  transformation  in  the  usual  way,  we  obtain 


204        OUTLINES  OF  PHYSICAL  CHEMISTRY 


•  •       (4) 

By  substituting  in  the  above  equation  corresponding  values  of 
a,  a  —  x  and  /  from  the  table  (p.  202),  we  obtain  the  values  of  k 
given  in  the  fourth  column  of  the  table,  the  average  value  being 
0-0437.  Since  k  is  constant  within  the  limits  of  experimental 
error,  it  follows  that  the  assumption  on  which  the  equation  is 
based,  that  the  rate  of  the  reaction  is  proportional  to  the 
concentration  of  the  peroxide,  is  justified. 

It  is  instructive  to  compare  the  accurate  value  of  k,  obtained 
by  means  of  the  integrated  equation  (4),  with  that  calculated 
from  the  differential  equation  (2),  taking  as  the  value  of  a  -  x 
the  average  value  during  an  interval.  If  we  choose  the  interval 
between  5  and  10  minutes,  dx  =  7*3  c.c.,  dt  =  5  minutes,  and 
the  mean  value  of  a  -  x  is  33*45  c.c.  Hence 

y  =  k  x  33*45, 

and  k  =  0-0436,  which  is  very  close  to  the  accurate  average 
value  0*0437. 

A  reaction  of  the  above  type,  in  which  only  one  mol  of  a 
single  substance  is  undergoing  change,  is  termed  a  unimolecular 
reaction  or  a  reaction  of  the  first  order,  k  is  termed  the  velocity 
constant,  and  is,  for  unimolecular  reactions,  independent  of  the 
units  in  which  the  concentration  is  expressed,  but  increases  con- 
siderably with  rise  of  temperature.  The  meaning  of  k  becomes 
clear  when  we  consider  the  initial  velocity  of  the  reaction. 
Under  these  circumstances,  the  general  equation 

dx\dt  =  k  (a  -  x) 

becomes  dxfdt  =  ka  =  0-04370  for  the  example  given  above. 
Otherwise  expressed,  the  initial  velocity  of  the  reaction  =  velo- 
city constant  x  initial  concentration.  If,  by  addition  of  fresh 
peroxide,  the  concentration  is  kept  throughout  at  its  initial 
value,  then  in  unit  time  (i  minute)  0*0437  of  a  or  over  4  per 
cent,  of  a  will  be  decomposed. 


VELOCITY  OF  REACTION.     CATALYSIS       205 

If  the  integrated  equation  (3)  is  written  in  the  form 
log  a  I  (a  -  x)  =  kt, 

we  see  that  the  left-hand  side  of  the  equation  only  becomes  in- 
finitely great  (a  =  x)  when  /  is  infinitely  great.  Hence,  for 
finite  values  of  t,  x  is  always  less  than  a,  in  other  words,  a 
chemical  reaction,  even  if  irreversible,  is  never  quite  complete. 

Other  Unimolecular  Reactions  —  Many  unimolecular  re- 
actions have  been  investigated,  among  the  more  interesting 
being  the  hydrolysis  of  cane  sugar  and  of  esters  under  the 
influence  of  acids.  The  hydrolysis  of  cane  sugar  to  dextrose 
and  laevulose  is  represented  by  the  equation 

CttHMOu  +  H2O  =  C6H12O6  +  C6H12O6, 

and  as  the  acid  remains  unaltered  at  the  end  of  the  reaction,  it 
does  not  occur  in  the  equation.  The  reaction  can  be  con- 
veniently followed  by  measuring  the  change  in  rotation  with  a 
polarimeter  (p.  66)  ;  as  cane  sugar  is  dextrorotatory  and  the 
mixture  of  dextrose  and  laevulose  laevorotatory,  the  rotation 
diminishes  steadily  as  the  reaction  progresses,  and  finally 
changes  sign. 

As  both  sugar  and  water  take  part  in  the  reaction,  the 
velocity  equation,  according  to  the  law  of  mass  action,  is 


j. 

As,  however,  water  is  present  in  great  excess,  its  concentra- 
tion, and  therefore  its  active  mass,  remain  practically  constant 
throughout  the  reaction,  and  the  equation  therefore  reduces  to 
one  of  the  first  order,  in  satisfactory  agreement  with  the  ex- 
perimental results. 

Similar   considerations    enable    us    to   understand    why   the 

acid  does  not  appear  in  the  velocity  equation.     It  is  true  that 

he  rate  of  the  reaction  depends  upon  the  concentration  of  acid 

present,  and  this,  if  necessary,  could  be  expressed  by  putting  in 

a  term  Cacid  °n  the  right-hand  side  of  the  velocity  equation. 


206       OUTLINES  OF  PHYSICAL  CHEMISTRY 

But  as  Cacid  does  not  change  in  the  course  of  the  reaction, 
the  only  effect  is  to  multiply  the  right-hand  side  of  the  equa- 
tion by  a  constant  amount  which,  under  ordinary  circumstances, 
we  may  consider  as  included  in  the  velocity  constant  k.  In  the 
same  way,  the  enzyme  concentration  in  the  example  quoted  on 
the  previous  page  is  included  in  the  velocity  constant,  and  the 
course  of  the  reaction  is  determined  by  the  peroxide  concentra- 
tion. 

The  hydrolysis  of  an  ester — for  example,  ethyl  acetate — in 
the  presence  of  excess  of  a  strong  acid,  such  as  hydrochloric 
acid,  is  represented  by  the  equation 

CH3COOC2H5  +  H2O  =  CH8COOH  +  C2H5OH, 

and  is  also  of  the  first  order,  as  the  active  mass  of  the  water 
is  constant.  The  reaction  may  readily  be  followed  by  removing 
a  portion  of  the  reaction  mixture  from  time  to  time  and  titrating 
with  dilute  alkali.  The  measurements  may  conveniently  be 
made  as  follows  :  To  40  c.c.  of  1/2  normal  hydrochloric  acid} 
previously  kept  in  a  100  c.c.  flask  for  some  time  at  25°,  2  c.c.  of 
methyl  acetate,  warmed  to  the  same  temperature,  is  added,  the 
mixture  shaken,  and  the  flask  well  corked  and  allowed  to  remain 
in  the  thermostat  at  constant  temperature.  At  first  every  20-30 
minutes,  and  then  at  longer  intervals,  2  c.c.  of  the  mixture  is 
removed  with  a  pipette,  diluted,  and  titrated  rapidly  with  N/io 
barium  hydroxide,  using  phenolphthalein  as  indicator.  The 
results  are  calculated  in  the  usual  way  by  substitution  in  equa- 
tion (i).  At  25°  the  value  of  k  for  this  reaction  is  0-0032. 

It  should  be  mentioned  that  it  is  not  necessary  to  take  for 
the  value  of  a  the  initial  concentration  of  the  reacting  sub- 
stance ;  the  calculation  of  the  velocity  constant  may  be  com- 
menced at  any  stage  in  the  reaction,  or  may  be  made  from 
titration  to  titration.  In  the  latter  case  the  integrated  equation 
for  a  reaction  of  the  first  order  is  of  the  form 

i       ,         a  -  x-, 

Iog10 -1  =0-4343^ 

to  —  f\  a  —  x^ 


VELOCITY  OF  REACTION.     CATALYSIS      207 

where  a  -  xl  and  a  -  x2  are  the  respective  concentrations  at 
the  times  tl  and  /2.  These  methods  of  calculation  gives  satis- 
factory results  when,  as  is  not  infrequently  the  case,  there  are 
irregularities  at  the  beginning  or  in  the  course  of  a  reaction. 

Bimolecular  Reactions  —  When  two  substances  react  and 
both  alter  in  concentration,  the  reaction  is  said  to  be  bimole- 
cular,  or  of  the  second  order.  If  the  initial  molar  concentration 
of  one  substance  is  a,  that  of  the  other  b,  and  x  the  amount 
transformed  in  the  time  /,  the  velocity  equation  is 


The  simplest  case  is  that  in  which  the  substances  are  present  in 
equivalent  quantities.     The  velocity  equation  then  becomes 


which,  on  integration,  gives  the  formula 


As  an  illustration  of  a  bimolecular  reaction,  the  hydrolysis  of  an 
ester  by  alkali  may  be  adduced,  a  reaction  which  has  been 
thoroughly  investigated  by  Warder,  Ostwald,  Arrhenius  and 
others.  For  ethyl  acetate  and  sodium  hydroxide,  the  equation 
is  as  follows  :  — 

CH3COOC2H5  +  NaOH  =  CH,COONa  +  C2H6OH. 

In  carrying  out  an  experiment,  1/20  mokr  solutions  of  ethyl 
acetate  and  of  sodium  hydroxide  are  warmed  separately  in  a 
thermostat  at  constant  temperature  (25°)  for  some  time,  equal 
volumes  of  the  solutions  are  then  mixed,  and  from  time  to  time 
a  portion  of  the  reaction  mixture  is  removed  and  titrated  rapidly 
with  dilute  hydrochloric  acid.  In  the  following  table  are  given 
some  results  obtained  by  Arrhenius  :  — 


208        OUTLINES  OF  PHYSICAL  CHEMISTRY 

1/50  molar  solution  at  24-7°.  J/1?0  molar  solution  at  247°. 


t  (min.) 

a-x 

k 

t  (min.)   a-x 

k 

0 

8-04 

— 

o     2*31 

— 

4 

5'30 

o'oi6o 

6 

•87 

o'oiyo 

6 

4-S8 

o'oi56 

12 

'57 

o'oiyo 

8 

3'9I 

©•0164 

18 

'35 

0*0171 

10 

3-5I 

o'oi6o 

24 

'20 

0-0167 

12 

3'12 

0*0162 

30 

'10 

o-oi63 

The  numbers  for  a  —  x  in  the  second  and  fifth  columns  re- 
present the  concentrations  of  sodium  hydroxide  (and  of  ethyl 
acetate)  expressed  as  the  number  of  c.c.  of  hydrochloric  acid 
required  to  neutralize  10  c.c.  of  the  reaction  mixture.  The 
reaction  is  very  rapid,  and  therefore  the  experimental  error 
is  somewhat  large  but  the  values  obtained  for  k  in  the  third 
and  sixth  columns  show  that  the  assumptions  on  which  formula 
(2)  is  based  are  justified. 

Another  bimolecular  reaction,  which  differs  from  the  former 
inasmuch  as  two  molecules  of  the  same  substance  react,  is  the 
transformation  of  benzaldehyde  to  benzoin  under  the  influence 
of  potassium  cyanide.  The  reaction  is  represented  by  the 
equation 

2C6H5CHO  =  C6H5CHOHCOC6H5, 

the  potassium  cyanide  remaining  unaltered  at  the  end  of  the 
reaction. 

When  the  reacting  substances  are  not  present  in  equivalent 
proportions,  the  calculation  is  somewhat  more  complicated.  On 
integrating  the  equation  dxjdt  =  k(a  -  x)(b  -  x),  we  obtain 
for  this  case 

i  b(a  —  x) 


In  order  to  illustrate  the  application  of  this  equation,  some 
results  obtained  by  Reicher  for  the  saponification  of  ethyl 
acetate  by  excess  of  alkali  may  be  adduced.  The  reaction  was 
followed  by  titrating  portions  of  the  reaction-  mixture  from  time 
to  time  with  standard  acid,  as  already  described,  and  the  excess 


VELOCITY  OF  REACTION.     CATALYSIS       209 

of  alkali  was  determined  by  titration  of  a  portion  of  the  solution 
after  the  ethyl  acetate  was  completely  saponified  (at  the  end  of 
twenty- four  hours). 

t  (min.).  a  -  x  b  -  x                       k 

(alkali  concentration).  (ester  concentration). 

O  61-95  47'03 

4-89  50-59  35-67               0-00093 

11*36  42*40  27-48               0-00094 

29-18  29*35  i4'43             0-00092 

oo  14*92  o 

It  is  important  to  note  that  the  value  of  k  for  a  bimolecular 
reaction  is  not,  as  the  case  of  a  unimolecular  reaction,  indepen- 
dent of  the  units  in  which  the  concentration  is  expressed.  If, 
for  example,  a  unit  i/nth  of  the  first  is  chosen,  the  value  of 

ix,  i          nx  i         x  i 

k  =  -  —, r  becomes  - 


a(a  -  x)  t  na.n(a-x)       t  a(a  -  x)  '  n 

so  that  the  value  of  k  diminishes  proportionally  to  the  increase 
of  the  numbers  expressing  the  concentrations.  The  truth  of 
this  statement  can  be  tested  by  means  of  the  data  for  ester 
saponification  due  to  Arrhenius.  If  the  titrations  are  made 
with  acid  of  half  the  strength  actually  used,  (n  =  2),  the 
numbers  expressing  the  concentrations  will  be  doubled,  and  it 
will  be  found  by  trial  that  the  value  of  k  becomes  half  that 
given  in  the  table. 

Trimolecular  Reactions — When  three  equivalents  take 
part  in  a  chemical  change,  the  reaction  is  termed  trimolecular, 
and  several  such  reactions  have  been  carefully  investigated.  If, 
as  before,  we  represent  the  initial  molar  concentrations  of  the 
reacting  substances  by  a,  b  and  c  respectively,  and  if  x  is  the 
proportion  of  each  transformed  in  the  time  /,  the  rate  of  reaction 
at  that  time  will,  according  to  the  law  of  mass  action,  be 
represented  by  the  differential  equation 

M 


210       OUTLINES  OF  PHYSICAL  CHEMISTRY 

^  =  k(a  -  x)(b  -  x)(c  -  x). 

Such  an  equation  is  somewhat  difficult  to  integrate,  and  we  will 
therefore  confine  ourselves  to  the  simple  case  in  which  the 
initial  concentrations  are  the  same.  The  equation  then  becomes 
dxjdt  =  k  (a  —  x)9,  which  on  integration  gives  for  k — 

_  i   x(2a  -  x) 
t  2a\a  -  xf 

Different  cases  arise  according  as  the  reacting  molecules  are  the 
same  or  different.  The  simplest  case,  in  which  the  three  re- 
acting molecules  are  the  same,  is  illustrated  by  the  condensation 
of  cyanic  acid  to  cyamelide,  represented  by  the  equation 

3HCNO  =  H3C8N303. 

A  case  where  two  only  of  the  reacting  molecules  are  the  same 
is  the  reaction  between  ferric  and  stannous  chlorides,  represented 
by  the  equation 

2FeCl3  +  SnCl2  =  SnCl4  +  2FeCl2. 

Finally,  the  reaction  between  ferrous  chloride,  potassium  chlorate 
and  hydrochloric  acid,  represented  by  the  equation 

6FeCl2  +  KC1O3  +  6HC1  =  6FeCl3  +  KC1  +  3H2O, 

has  been  shown  by  Noyes  and  Wason  to  be  proportional  to  the 
respective  concentrations  of  the  three  reacting  substances,  and 
is  therefore  of  the  third  order. 

As  an  illustration  of  a  trimolecular  change,  some  of  Noyes' 
results  for  the  reaction  between  ferric  and  stannous  chlorides 
are  given  in  the  table.  The  reacting  substances  were  mixed 
together  at  constant  temperature,  and  from  time  to  time  a 
measured  quantity  of  the  solution  was  removed  with  a  pipette, 
the  stannous  chloride  decomposed  with  mercuric  chloride,  and 
the  ferrous  salt  still  remaining  titrated  with  potassium  per- 
manganate in  the  usual  way. 


VELOCITY  OF  REACTION.     CATALYSIS       211 

SnCl2  =  FeCl3  =  0-0625  normal  =  a. 
t  (min.)  a  -  x  x  k 

0  0*0625  o 

1  0*04816  0*01434  88 
3              0*03664              0*02586  81 
7              0*02638              0*03612              84 

17  0*01784  0*04502  89 

25  0*01458  0*04792  89 

Reactions  of  Higher  Order.  Molecular  Kinetic  Con- 
siderations —  Whilst  reactions  of  the  first  and  second  order 
are  very  numerous,  reactions  of  the  third  order  are  compara- 
tively seldom  met  with,  and  reactions  of  a  still  higher  order  are 
practically  unknown.  This  is  at  first  sight  surprising,  as  the 
equations  representing  many  chemical  reactions  indicate  that  a 
considerable  number  of  molecules  take  part  in  the  change,  and 
a  correspondingly  high  order  of  reaction  is  to  be  expected.  The 
oxidation  of  ferrous  chloride  by  potassium  chlorate  in  acid  solu- 
tion, for  example,  is  usually  represented  by  the  equation 

6FeCl2  +  KC1O3  +  6HC1  =  6FeCl3  +  KC1  +  3H2O. 
Applying  the  law  of  mass  action  (p.  143),  we  have  therefore 


that  is,  the  reaction  should  be  of  the  thirteenth  order,  whilst  it 
is  actually  of  the  third  order  (p.  210).  To  account  for  this 
result,  it  has  been  suggested  by  'van't  Hoff  that  complicated 
chemical  reactions  take  place  in  stages,  and  that  the  reaction 
whose  speed  is  actually  measured  is  one  in  which  only  two  or 
three  molecules  take  part,  the  velocity  of  the  other  reactions 
being  very  great  in  comparison.  This  view  is  further  considered 
in  the  next  section. 

The  molecukr  theory  throws  a  good  deal  of  light  on  this 
question.  On  the  assumption  that  the  rate  of  chemical  reaction 
is  proportional  to  the  number  of  collisions  between  the  reacting 
molecules  (p.  160),  it  follows  that  in  a  trimolecular  reaction  the 


212        OUTLINES  OF  PHYSICAL  CHEMISTRY 

three  reacting  molecules  must  collide  simultaneously  to  produce 
a  chemical  change.  The  probability  of  such  a  collision  is  ex- 
tremely small  compared  with  that  between  two  molecules  ;  there- 
fore, if  at  all  possible,  the  reaction  will  take  place  between  two 
molecules  or  by  the  change  of  a  single  molecule.  The  proba- 
bility of  the  simultaneous  collision  of  four  molecules  is  so  small 
as  to  be  almost  negligible. 

Reactions  in  Stages — It  has  just  been  pointed  out  that 
many  reactions  which  are  represented  by  rather  complicated 
equations  prove  on  investigation  to  be  of  the  second  or  third 
order,  which  seems  to  show  that  the  reaction,  the  speed  of  which 
is  being  measured,  is  in  reality  a  comparatively  simple  one.  When 
a  chemical  change  takes  place  in  stages,  a  little  consideration 
shows  that  it  is  the  slowest  of  a  series  of  reactions  which  is  the 
determining  factor  for  the  observed  velocity.  This  process  has 
been  fittingly  compared  by  Walker  to  the  sending  of  a  telegram ; 
the  time  which  elapses  between  dispatch  and  receipt  is  con- 
ditioned almost  entirely  by  the  time  taken  by  the  messenger 
between  receiving-office  and  destination,  as  that  is  by  far  the 
slowest  in  the  successive  stages  of  transmission. 

An  instructive  example  of  a  reaction  which  takes  place  in 
stages  is  the  burning  of  phosphorus  hydride  in  oxygen,  investi- 
gated in  van't  HofFs  laboratory  by  van  der  Stadt.  The  change 
is  usually  represented  by  the  equation 

2PH3  +  402  =  P205  +  3H20, 

according  to  which  it  would  be  a  reaction  of  the  sixth  order 
whilst  the  rate  was  actually  found  to  be  proportional  to  the 
respective  concentrations  of  the  two  gases,  the  reaction  being 
therefore  of  the  second  order.  On  allowing  the  gases  to  mix 
gradually  by  diffusion,  it  was  then  found  that  the  first  stage  of 
the  reaction  is  represented  by  the  equation 

PH3  +  02  =  HP02  +  H2 
— that  of  a  bimolecular  reaction — the  subsequent  changes  by 


VELOCITY  OF  REACTION.     CATALYSIS       213 

which  water  and  phosphorus  pentoxide  are  produced  being  very 
rapid  in  comparison. 

Many  other  reactions  proceed  in  stages,  and  in  some  cases 
evidence  as  to  the  nature  of  the  intermediate  compounds  has 
been  obtained.  Thus  the  reaction  between  hydrobromic  and 
bromic  acid,  usually  represented  by  the  equation 

HBr03  +  sHBr  =  3H2O  +  3Br2, 

is  bimolecular  in  the  presence  of  excess  of  acid,  and  it  is  probable 
that  the  first  stage  (the  slow  reaction)  is  as  follows  : — 

HBrO3  +  HBr  =  HBrO  +  HBrO2, 

the  subsequent  changes,  by  which  bromine  and  water  are  finally 
produced,  being  comparatively  rapid. 

It  is  very  probable  that  the  equations  which  we  ordinarily 
use  represent  only  the  initial  and  final  stages  in  a  series  of 
changes,  and  the  determination  of  the  "  order  "  of  the  reaction 
is  one  of  the  most  important  methods  for  elucidating  the  nature 
of  the  relatively  unstable  intermediate  compounds. 

Determination  of  the  Order  of  a  Reaction — Three  im- 
portant methods  which  are  largely  used  in  determining  the  order 
of  reactions  may  be  mentioned  here. 

(a)  The  Method  of  Integration — According  to  this  method, 
the  values  of  k  given  by  the  integrated  equations  for  reactions 
of  the  first,  second  and  third  order  are  calculated  from  the  ex- 
perimental results,  and  the  order  of  the  reaction  is  that  in  which 
constant  values  are  obtained  for  k.  The  method  can  be  applied 
to  the  numbers  obtained  for  the  reaction  between  equivalent 
amounts  of  ethyl  acetate  and  sodium  hydroxide,  when  it  will  be 
found  that  the  values  for  k,  calculated  from  the  equation  k  = 
ijt\ogal(a  -  x),  continually  decrease  throughout  the  reaction; 
the  values  obtained  with  an  equation  of  the  third  order  continu- 
ally increase,  and  only  for  the  equation  k  =  i//.#/0(a  -  x)  is  k 
actually  constant.  The  disadvantage  of  this  method  is  that 
disturbing  causes,  such  as  secondary  reactions  or  the  influence 
of  the  reaction  products  on  the  velocity,  may  so  complicate  the 


214       OUTLINES  OF  PHYSICAL  CHEMISTRY 

results  that  a  decision  as  to  the  order  of  the  reaction  is  impossible 
or  an  erroneous  conclusion  may  be  drawn. 

(b)  Ostwald's  "  Isolation  "  Method  —  It  has  already  been 
pointed  out  that  if  one  or  more  of  the  reacting  substances  is 
taken  in  great  excess,  so  that  their  concentration  does  not  alter 
appreciably  during  the  reaction,  the  velocity,  as  far  as  these 
substances  is  concerned,  may  be  regarded  as  constant.  It  is 
on  this  principle  that  the  "  isolation  "  method  is  based.  Each 
of  the  reacting  substances  in  turn  is  taken  in  small  concentra- 
tion and  all  the  others  in  excess,  and  the  relation  between  the 
reaction  velocity  and  the  concentration  of  the  substance  present 
in  small  amount  determined  experimentally.  As  an  example, 
we  will  consider  the  reaction  between  potassium  iodide  and 
iodate  in  acid  solution,  investigated  by  Dushman.1  Regarding 
the  action  of  the  acid  as  due  to  H*  ions  (p.  125),  the  reaction 
velocity,  according  to  the  law  of  mass  action,  must  be  repre- 
sented by  the  equation 


When  iodide  and  acid  are  used  in  large  excess,  the  velocity  is 
proportional  to  the  iodate  concentration  («j  =  i)  ;  with  a  large 
excess  of  iodate  and  acid  it  is  proportional  to  the  square  of  the 
iodide  concentration  (nz  =  2)  ;  and  finally,  when  iodide  and 
iodate  are  in  large  excess,  it  is  proportional  to  the  square  of 
the  acid  concentration  (ns  —  2).  Hence  the  velocity  equation 
becomes 

§  =  *P<VF]tH-]«, 

and  when  neither  of  the  reagents  is  present  in  great  excess,  is 
of  the  fifth  order. 

(c)  Time  taken  to  Complete  the  same  Fraction  of  the  Reaction 
—  Measurements  are  made  with  definite  concentrations  of  the 
reacting  substances,  and  with  double  and  treble  those  con- 

13f.  Physical  Chem.,  1904,  8,  453.  As  the  rate  of  reaction  does  not 
depend  upon  the  particular  iodate  or  iodide  used,  we  employ  the  formulae 
for  the  iodate  ion  lO,'  and  the  iodide  ion  I'. 


VELOCITY  OF  REACTION.     CATALYSIS       215 

centrations,  and  the  times  taken  to  complete  a  certain  stage  (say 
one-third)  of  the  reaction  noted.  The  order  of  the  reaction 
can  then  be  determined  from  the  following  considerations 
(Ostwald)  :— 

(1)  For  a  reaction  of  the  first  order  the  time  taken  to  com- 
plete a  certain  fraction  of  the  reaction  is  independent  of  the 
initial  concentration. 

(2)  For  a  reaction  of  the  second  order,  the  time  taken  to 
complete  a  certain  fraction  of  the  reaction  is  inversely  propor- 
tional to  the  initial  concentration,  e.g.,  if  the  concentration  is 
doubled,  the  time  taken  to  complete  a  certain  fraction  of  the 
reaction  is  halved. 

(3)  In  general,  for  a  reaction  of  the  nth  order,  the  times 
taken  to  complete  a  certain  fraction  of  the  reaction  are  inversely 
proportional  to  the    (n  -  i)  power   of  the   initial   concentra- 
tion. 

In  the  experiments  by  Arrhenius,  quoted  on  page  208,  it  will 
be  noticed  that  in  the  second  experiment,  in  which  the  con- 
centrations are  less  than  J  of  those  in  the  first  experiment,  the 
time  taken  to  complete  half  the  reaction  is  about  three  times 
as  long  in  the  former  case  as  in  the  latter. 

Complicated  Reaction  Velocities — In  the  present  chapter, 
it  has  so  far  been  assumed  that  chemical  reactions  proceed  only 
in  one  direction,  and  are  ultimately  complete,  or  practically 
so,  but  in  many  cases  these  conditions  are  not  fulfilled  and 
the  course  of  the  reaction  is  complicated.  The  more  im- 
portant disturbing  causes  are  (a)  side  reactions;  (b)  counter 
reactions  ;  (c)  consecutive  reactions.  Each  of  these  will  be 
briefly  considered. 

(a)  Side  Reactions — In  this  case  the  same  substances  react 
in  two  (or  more)  ways  with  formation  of  different  products  ;  in 
general  the  reactions  proceed  side  by  side  without  influencing 
each  other.  An  example  is  the  action  of  chlorine  on  benzene,1 
which  may  substitute  or  form  an  additive  product  according  to 
the  equations 

1  Slator,  Trans.  Chem.  Soc.,  1903,  83,  729. 


216        OUTLINES  OF  PHYSICAL  CHEMISTRY 

(1)  C6H6  +  C12  =  C6H5C1  +  HC1, 

(2)  C6H6  +  3C12  =  C6H6C16. 

The  relative  amounts  of  the  products  formed  in  side  reactions 
depend  on  the  conditions  of  the  experiment,  and  it  is  usually 
possible  so  to  choose  the  conditions  that  one  of  the  reactions 
greatly  predominates  and  can  be  investigated  independently. 

(&}  Counter  Reactions  —  This  term  is  applied  when  the  pro- 
ducts of  a  reaction  interact  to  reproduce  the  original  substances, 
so  that  a  state  of  equilibrium  is  finally  reached,  all  the  re- 
acting substances  being  present  (p.  201).  Using  the  same 
terminology  as  before,  the  rate  of  formation  of  an  ester,  for 
example,  will  be  represented  by  the  differential  equation 

dx 

-—  =  k(a  -  x)(b  -  x)  -  k-fc  +  x}(d  +  x). 

The  conditions  can,  however,  usually  be  chosen  in  such  a  way 
that  either  the  direct  or  the  reverse  reaction  predominates,  and 
the  values  of  k  and  k^  can  thus  be  determined  separately.  In 
this  way  it  has  been  shown  experimentally  by  Knoblauch1  that 
the  ratio  k-Jk  =  K,  the  equilibrium  constant,  as  the  theory 
requires  (p.  158). 

(f)  Consecutive  Reactions  —  Consecutive  reactions  are  those 
in  which  the  products  of  a  chemical  change  react  with  each 
other  or  with  the  original  substances  to  form  a  new  substance 
or  substances.  They  appear  to  be  of  very  frequent  occurrence 
(p.  212).  A  good  example  is  the  saponification  of  ethyl  succi- 
nate,  investigated  by  Reicher.  It  proceeds  in  the  following  two 
stages  :  — 

(  i  )  C2H4(COOC2H5)2  +  NaOH  =  C2 


f^  r  w 

(2)  C2H4  +  NaOH  =  C2H5(COONa) 


the  product  of  the  first  reaction,  ethyl  sodium  succinate,  re- 
acting further  with  sodium  hydroxide  to  form  the  normal  sodium 
salt. 

1  Zeitsch.  physikal.  Chem.,  1897,  22,  268. 


VELOCITY  OF  REACTION.     CATALYSIS       217 

It  is  important  to  remember  that  when  one  of  the  reactions 
is  very  slow  compared  with  the  others,  good  constants  cor- 
responding with  the  slow  reaction  are  obtained,  but  when  the 
rates  are  not  very  different,  the  observed  velocity  does  not 
correspond  with  any  simple  order  of  reaction. 

CATALYSIS 

General — We  have  already  met  with  instances  in  which  the 
rate  of  reaction  is  greatly  increased  by  the  presence  of  a  third 
substance,  which  itself  is  unaltered  at  the  end  of  the  reaction. 
Thus  cane  sugar  is  hydrolysed  very  slowly  by  water  alone,  but 
the  change  is  greatly  accelerated  by  the  addition  of  acids.  Such 
phenomena  are  termed  catalytic,  and  the  substance  which  exerts 
the  catalytic  or  accelerating  action  is  termed  a  catalysor  or 
catalyst.  Ostwald,  to  whom  much  of  our  knowledge  of  catalytic 
actions  is  due,  defines  a  catalyst  as  "  a  substance  which  alters 
the  velocity  of  a  reaction,  but  does  not  appear  in  the  end 
products  ".  From  the  point  of  view  of  the  quantitative  treat- 
ment of  reaction  velocities,  it  is  important  to  note  that  the  equa- 
tions already  established  remain  valid  in  the  presence  of  catalysts, 
the  only  effect  of  the  latter  being  to  alter  the  value  of  the  velocity 
constant,  k.  The  acceleration  produced  by  a  catalyst  is  in  the 
majority  of  cases  proportional  to  the  amount  of  the  latter  added.1 

Characteristics  of  Catalytic  Actions — From  the  above  it 
will  be  seen  that  the  term  catalysis  does  not  include  any  explana- 
tion of  the  observed  phenomena  ;  it  is  merely  a  classification  of 
reactions  which  have  certain  features  in  common.  In  order  to 
make  clear  the  exact  bearing  of  the  term,  some  characteristics 
of  catalytic  actions  will  now  be  adduced. 

(a)  The  catalyst  is  usually  present  in  relatively  small  concen- 
tration. This  is,  of  course,  connected  with  the  fact  that  it  is 

1  One  or  two  exceptions  to  this  rule  are  known ;  for  example,  the  ac- 
celerating influence  of  iodine  monochloride  on  the  rate  of  reaction  between 
chlorine  and  benzene  is  proportional  to  the  square  of  the  concentration  of 
the  catalyst  (Slator,  Zeitsch.  physikal.  Chem.,  1903,  45,  513). 


2i8        OUTLINES  OF  PHYSICAL  CHEMISTRY 

not  used  up  during  the  reaction,  so  that  a  relatively  small  pro- 
portion of  catalyst  can  effect  the  transformation  of  large  amounts 
of  the  substance  acted  on.  An  apparent  contradiction  to  this 
rule  (as  regards  the  small  concentration  of  the  catalyst)  is  the 
influence  of  the  medium  on  the  rate  of  reaction  (p.  22/),  but 
this  can  scarcely  be  termed  a  true  catalytic  action. 

(b]  The  catalyst  does  not  start  a  reaction,  but  only  accelerates 
a  change  which  can  proceed  of  itself,  though  perhaps  extremely 
slowly — Although  there  is  some  difference  of  opinion  with 
regard  to  the  general  validity  of  this  statement,  it  is  now  fairly 
widely  accepted,  and  seems  to  derive  support  from  thermodyna- 
mical  considerations.  As  an  illustration,  we  may  consider  the 
combination  of  hydrogen  and  oxygen  to  form  water.  It  is  well 
known  that  the  mixed  gases  can  be  kept  at  the  ordinary  tem- 
perature for  an  almost  indefinite  time  without  any  apparent 
combination,  but  when  brought  in  contact  with  platinum  they 
combine  fairly  rapidly.  It  might  at  first  sight  be  supposed  that 
the  platinum  actually  initiates  the  combination.  However,  when 
the  gases  are  heated  alone  at  440°,  they  combine  with  a  measur- 
able velocity,  and  at  lower  temperatures  still  combination  can  be 
observed  on  long  heating.  Since  the  rate  of  reaction  diminishes 
greatly  with  fall  of  temperature  (p.  225),  it  can  readily  be  under- 
stood that  the  rate  of  combination  may  be  so  slow  at  the  ordinary 
temperature  as  not  to  be  measurable. 

The  alternative  view  is  that  the  hydrogen  and  oxygen  are 
not  entering  into  combination  at  all  at  the  ordinary  temperature, 
that  they  are  in  a  condition  of  unstable  or  false  equilibrium  and 
that  the  catalyst  actually  initiates  the  combination.  A  direct 
decision  between  these  alternative  hypotheses  is  difficult,  but 
there  is  some  evidence  of  the  existence  of  false  equilibria. 
For  example,  oxygen  at  fairly  low  pressures  acts  readily  on 
phosphorus,  but  when  the  pressure  reaches  a  certain  value, 
which  depends  on  the  temperature,  the  reaction  stops  com- 
pletely, and  there  is  an  apparent  equilibrium.  The  conditions 
determining  this  curious  phenomenon  are  not  well  understood. 


VELOCITY  OF  REACTION.     CATALYSIS       219 

The  limit  of  pressure  above  which  oxidation  does  not  occur 
depends  on  the  amount  of  moisture  present,  and  doubtless  also 
on  the  presence  of  traces  of  impurities. 

(c)  The  presence  of  a  catalyst  does  not  affect  the  equilibrium  ; 
it  alters  the  speed  of  the  direct  and  inverse  actions  to  the  same 
extent — The  truth  of  the  first  part  of  this  statement  follows  at 
once  from  the  principle  of  the  conservation  of  energy ;  provided 
that  the  catalyst  is  not  combined  with  any  of  the  products  when 
the  reaction  is  complete,  it  does  not  produce  any  change  in  the 
energy  content  of  the  system.  It  has  also  been  proved  experi- 
mentally in  many  cases.  Thus  Kiister  found  that  in  the  reaction 
represented  by  the  equation  2SO2  +  O2  =  2SO3,  the  same  equi- 
librium point  was  reached  in  the  presence  of  such  different 
catalysts  as  platinum,  ferric  oxide  and  vanadium  pentoxide. 

The  second  part  of  the  above  statement,  that  the  catalyst 
alters  the  speed  of  the  direct  and  inverse  actions  to  the  same 
extent,  is  a  direct  consequence  of  the  first  part.  It  has  already 
been  shown  that  the  equilibrium  constant  K  =  k^k,  so  that,  if 
k  is  increased,  k^  must  increase  in  the  same  ratio  in  order  that 
K  may  remain  constant.  In  accordance  with  this  rule,  Baker 
found  that  in  the  complete  absence  of  water  vapour,  neither  of 
the  actions  represented  by  the  oppositely-directed  arrows  in  the 
equation  NH4C1^NH3  +  HC1  took  place,  but  the  presence  of 
moisture  accelerated  the  dissociation  of  ammonium  chloride,  as 
well  as  its  formation  from  its  components. 

Examples  of  Catalytic  Action.  Technical  Importance 
of  Catalysis — There  appear  to  be  very  few  chemical  changes 
which  cannot  be  accelerated  by  the  addition  of  certain  sub- 
stances, and  many  catalysts  are  known.  Acids  as  a  class 
accelerate  many  chemical  changes,  more  particularly  those  of 
hydrolysis,  such  as  the  hydrolytic  decomposition  of  cane  sugar, 
of  amides,  esters,  etc.,  but  not  of  chloroacetic  acid.1  As  the 
catalytic  power  is  in  general  proportional  to  the  extent  to  which 
the  acid  is  split  up  into  its  ions,  we  ascribe  the  catalytic  pro- 

1  Senter,  Trans.  Chem.  Society,  1907,  91,  460. 


220       OUTLINES  OF  PHYSICAL  CHEMISTRY 

perty  to  that  which  is  common  to  all  acids,  namely,  hydrogen 
ions.  Only  in  dilute  solution  is  there  exact  proportionality 
between  hydrogen  ion  concentration  and  catalytic  power. 
In  stronger  solutions,  for  a  reason  as  yet  unexplained,  the 
catalytic  activity  increases  more  rapidly  than  the  hydrogen 
ion  concentration. 

Bases  in  some  cases  also  exert  a  catalytic  effect,  as  in  the 
condensation  of  acetone  to  diacetonylalcohol,  represented  by 
the  equation 

2CH3COCH3  =  CH3COCH2C(CH3)2OH  ; 

in  this  case  the  acceleration  is  proportional  to  the  OH'  ion 
concentration.  Bases  have  also  a  powerfully  accelerating  action 
in  certain  isomeric  changes  of  organic  compounds.1 

The  rare  metals,  more  particularly  finely-divided  platinum, 
also  accelerate  many  chemical  reactions,  especially  oxidation 
reactions.  Thus  platinum  is  used  commercially  in  the  manu- 
facture of  sulphuric  acid  as  a  catalyst  for  the  reaction  2SO2  + 
O2  =  2SO3,  as  well  as  in  the  oxidation  of  methyl  alcohol  to 
formaldehyde  and  of  ammonia  to  nitric  acid.  Hydrogen  and 
oxygen  also  combine  to  form  water  at  the  ordinary  temperature 
in  the  presence  of  finely-divided  platinum,  and  the  same  catalyst 
also  accelerates  the  splitting  up  of  hydrogen  peroxide  into  water 
and  oxygen.  The  latter  reaction  has  been  investigated  fully 
by  Bredig  and  his  pupils,  who  used  the  platinum  in  so-called 
"  colloidal "  solution.  The  solution  was  obtained  by  passing 
the  electric  arc  between  platinum  poles  immersed  in  cold 
water ;  under  these  circumstances  the  metal  was  torn  from  the 
poles  and  remained  suspended  in  the  water  in  a  very  finely- 
divided  condition  (p.  232). 

Another  interesting  catalyst  is  water  vapour.  It  has  been 
found,  for  example,  that  thoroughly  dried  carbon  monoxide  does 
not  burn  in  thoroughly  dried  air,  but  when  a  trace  of  moisture 
is  present,  combination  takes  place  at  once.  Reference  has 

1  Lowry  and  Magson,  Trans.  Chem   Society,  1908,  93,  107. 


VELOCITY  OF  REACTION.     CATALYSIS       221 

already  been  made  to  the  fact  that  in  the  complete  absence 
of  moisture  ammonium  chloride  can  be  volatilised  without 
dissociation,  and  under  the  same  circumstances  ammonia  and 
hydrogen  chloride  do  not  combine.  As  the  water  does  not 
occur  in  the  equation,  it  acts  as  a  catalytic  agent,  but  its  mode 
of  action  is  quite  unknown. 

The  importance  of  catalysis  for  technical  processes  will  be 
clear  from  the  above.  Many  important  technical  reactions  are 
very  slow,  and  the  mixture  has  to  be  kept  for  a  long  period  at 
a  high  temperature  to  complete  them,  which  adds  much  to  the 
cost  of  production.  By  using  a  suitable  catalyst,  the  reaction 
may  be  completed  at  a  much  lower  temperature,  and  in  a  much 
shorter  time.  As  an  illustration,  the  oxidation  of  naphthalene 
to  phthalic  acid  by  means  of  sulphuric  acid — an  important  step 
in  the  manufacture  of  indigo — may  be  referred  to.  Under 
ordinary  circumstances,  the  reaction  is  slow  even  at  high  tem- 
peratures. Owing  to  the  accidental  breaking  of  a  thermometer 
on  one  occasion  when  the  reagents  were  being  heated  together 
a  little  mercury  fell  into  the  mixture,  and  the  observation  that 
the  reaction  then  proceeded  much  more  rapidly  led  to  the  dis- 
covery that  mercury  was  a  catalyst  for  the  reaction,  and  the 
whole  process  was  thus  rendered  commercially  successful.1  The 
use  of  copper  salts  in  the  Deacon  process — production  of 
chlorine  by  oxidation  of  hydrogen  chloride  with  free  oxygen — 
and  of  oxides  of  nitrogen  in  the  manufacture  of  sulphuric  acid, 
are  other  examples  of  technical  catalysis. 

Biological  Importance  of  Catalysis.  Enzyme  Re- 
actions— Catalysis  is  also  of  great  importance  in  physiology 
and  allied  subjects,  as  the  majority  of  the  changes  taking  place 
in  the  living  organism  are  accelerated  by  those  organic  catalysts 
— the  enzymes.  When  Berzelius  brought  forward  the  concep- 
tion of  catalysis,  he  adduced  among  other  illustrations  the 
hydrolysis  of  cane  sugar  by  invertase,  and  the  hydrolysis  of 
starch  in  the  presence  of  an  extract  of  malt.  It  is  now 
generally  recognised  that  these  and  allied  changes,  such  as 
1  Berichte,  1900,  33,  Appendix. 


222        OUTLINES  OF  PHYSICAL  CHEMISTRY 

alcoholic  fermentation  of  certain  sugars,  are  due  to  the  action 
of  catalysts  of  animal  or  vegetable  origin  which  can  be  separated 
from  the  living  cells  without  losing  their  activity,  an  d  which  are 
termed  enzymes. 

In  recent  years  much  progress  has  been  made  with  the 
investigation  of  enzyme  reactions,  and  although  little  or  nothing 
is  known  as  to  the  nature  of  the  catalysts  themselves,  no 
enzyme  having  so  far  been  isolated  in  a  state  of  purity,  the  laws 
followed  by  many  enzymes  have  been  satisfactorily  elucidated. 
In  general  it  may  be  said  that  enzymes  behave  like  inorganic 
catalysts,  but  there  are  certain  characteristic  differences.  Just 
as  in  the  case  of  an  inorganic  catalyst,  the  acceleration  pro- 
duced by  an  enzyme  is  in  the  first  instance  proportional  to  its 
concentration.  The  dependence  of  the  speed  of  the  reaction 
on"  the  concentration  of  the  substance  acted  on  is,  however, 
not  so  simple.  To  take  a  typical  illustration,  the  rate  of 
hydrolysis  of  cane  sugar  in  the  presence  of  a  constant  concen- 
tration of  invertase  increases  with  the  concentration  of  the  sugar 
in  dilute  solution,  but  beyond  a  certain  concentration  of  sugar, 
further  addition  of  the  latter  has  no  effect  on  the  rate  of  the 
reaction.  In  contrast  to  this  behaviour,  the  rate  of  inversion 
of  cane  sugar  in  the  presence  of  a  constant  concentration  of 
acid  increases  with  the  sugar  concentration  as  far  as  the  reaction 
has  been  followed. 

As  in  the  case  of  other  catalysts,  we  may  expect  that  the 
enzyme  will  accelerate  both  the  direct  and  inverse  actions 
when  the  reaction  is  reversible.  The  experiments  of  Croft  Hill, 
Emmerling,  Kastle x  and  others,  have  shown  that  this  expectation 
is  justified. 

Mechanism  of  Catalysis — The  nature  of  catalysis  becomes 

1  Kastle  and  Loevenhart  have  shown  that  the  reactions  represented  by 
the  upper  and  lower  arrows  in  the  equation 

C2H5OH  +  C3H7COOH  ^  C3H7COOC2H5  +  H2O 

(formation  and  hydrolysis  of  ethyl  butyrate)  are  both  accelerated  by  lipase, 
the  enzyme  which  effects  the  hydrolysis  of  fats  (Amer.  Chem.  y.,  1900, 
24,  491). 


VELOCITY  OF  REACTION.     CATALYSIS       223 

somewhat  clearer  when  we  represent  reaction  velocity,  in  a 
manner  analogous  to  Ohm's  law,  by  means  of  the  equation 

Driving  force 
Velocity  =  —^ — r-5-     —  • 
Resistance 

The  driving  force  of  a  chemical  reaction  is  the  same  thing  as 
the  free  energy  of  the  system  (p.  149);  of  the  resistance  little 
or  nothing  is  known.  It  is  clear  from  the  above  equation  that 
the  velocity  can  be  altered  in  two  ways,  by  increasing  the 
driving  force  and  by  lessening  the  resistance.  A  catalyst  can- 
not to  any  extent  affect  the  amount  of  energy  in  the  system, 
and  we  must  therefore  assume  that  in  some  way  it  increases 
the  velocity  by  diminishing  the  resistance.  Ostwald  compares 
the  action  of  a  catalyst  to  that  of  oil  on  a  machine,  and  it  is 
evident  that  the  analogy  is  far-reaching. 

It  may  be  asked  whether  all  catalytic  accelerations  are  due 
to  a  common  cause.  This  is  very  unlikely ;  it  is  much  more 
probable  that  the  mechanism  of  the  acceleration  varies  with 
the  nature  of  the  catalyst  and  with  that  of  the  reacting  sub- 
stances. The  suggestion  of  Liebig,  that  the  catalyst  sets  up 
certain  molecular  vibrations  which  lead  to  chemical  changes, 
has  proved  quite  unfruitful.  So-called  explanations  of  this 
nature,  though  often  employed  even  at  the  present  day,  are 
bad  in  principle,  as  we  know  very  little  of  the  nature  of  molecular 
vibrations.  It  is,  however,  quite  justifiable  to  inquire  into  the 
mechanism  of  catalytic  actions,  in  so  far  as  it  can  be  elucidated 
by  experimental  investigation,  and  in  recent  years  some  light 
has  been  thrown  on  this  subject. 

An  explanation  of  catalytic  acceleration  which  is  much 
favoured  is  that  it  depends  on  the  formation  of  intermediate 
compounds  of  the  catalyst  with  the  reacting  substances.  A 
reaction  represented  by  the  equation  A  +  B  =  AB  may  pro- 
ceed very  slowly  directly,  but  in  the  presence  of  a  catalyst  C  it 
may  proceed  in  the  following  two  stages  : — 

(a)  A  +  C  =  AC,  (b)  AC  +  B  =  AB  +  C, 


224       OUTLINES  OF  PHYSICAL  CHEMISTRY 

much  more  rapidly  to  the  same  final  products.  For  example, 
it  is  known  that  the  reaction  SO2  -t-  O  =  SO3  is  a  slow  one, 
and  the  accelerating  effect  of  nitric  oxide  on  the  combination 
may  be  represented  in  the  following  stages  : — 

(a)  NO  +  O  =  NO2 ;  (6)  SO2  +  NO2  =  SO3  +  NO. 
This  explanation  of  the  action  of  the  oxides  of  nitrogen  was 
suggested  more  than  a  century  ago  by  Clement  and  Desormes, 
and  remains  the  most  plausible  one  at  the  present  day.  It  is 
possible  that  the  finely-divided  metals  act  as  catalytic  agents 
mainly  in  a  physical  manner.  In  virtue  of  their  large  surface 
these  metals  condense  gases  and  to  some  extent  dissolved  sub- 
stances, and  the  local  increase  of  concentration  thus  produced 
must  greatly  increase  the  rate  of  chemical  change.  Similar 
considerations  may  explain  the  catalytic  effect  of  certain 
enzymes.  A  chemical  explanation  of  the  action  of  finely-divided 
metals  and  of  enzymes — based  on  the  formation  of  intermediate 
compounds — is,  however,  to  be  preferred. 

Nature  of  the  Medium — The  rate  of  a  chemical  change 
depends  greatly  on  the  nature  of  the  medium  in  which  it  takes 
place,  but  the  way  in  which  the  influence  is  exerted  is  quite 
unknown.  The  most  complete  data  on  this  subject  are  due 
to  Menschutkin,  who  determined  the  rate  of  combination  of 
triethylamine  and  ethyl  iodide,  represented  by  the  equation 

(C2H6)3N  +  C2H5I  =  (C2H5)4NI 

in  more  than  twenty  solvents  at  100°  A  few  typical  results 
are  given  in  the  accompanying  table,  in  which  £,  as  usual, 
represents  the  velocity  constant  : — 

Solvent.  k.  Dielectric  Constant. 

Hexane  0*00018  1*86  (12 '3°) 

Ethyl  ether  0*000757  4-36(18°) 

Benzene  0*00584  2*26  (19°) 

Ethyl  alcohol  0*0366  21*7     (15°) 

Methyl  alcohol  0*0516  32*5    (16°) 

Acetone  0*0608  21*8    (15°) 


VELOCITY  OF  REACTION.     CATALYSIS       225 

It  will  be  seen  that  the  rate  varies  enormously  with  change  of 
medium  ;  thus  the  ratio  of  the  velocities  in  hexane  and  acetone 
is  approximately  i  :  340. 

It  is  interesting  to  inquire  whether  there  is  any  other  pro- 
perty of  the  different  media  which  is  parallel  to  the  effect  on 
the  reaction  velocity.  It  was  suggested  on  theoretical  grounds 
by  J.  J.  Thomson,  and  somewhat  later  by  Nernst,  that  the 
"  dissociating  power  of  the  medium "  must  be  greater  the 
higher  its  specific  inductive  capacity  or,  to  use  the  more 
modern  term,  its  dielectric  constant.  The  dielectric  constants 
of  the  media  are  given  in  the  third  column  of  the  table,  and 
it  will  be  seen  that  there  is  a  distinct  parallelism,  though  not 
direct  proportionality,  between  dielectric  constant  and  reaction 
velocity.  This  question  will  be  again  referred  to  at  a  later  stage. 

Even  a  small  change  in  the  medium  has  sometimes  a  re- 
markable effect  on  the  rate  of  reaction.  Thus  it  has  recently 
been  shown  that  the  rate  of  reaction  between  pure  sulphuric 
acid  and  oxalic  acid  is  reduced  to  1/17  of  its  original  value 
by  the  addition  of  o'i  per  cent,  of  water  to  the  reaction 
mixture. 

On  the  other  hand,  a  considerable  alteration  in  the  medium 
may  have  very  little  effect  on  the  velocity.  Thus  the  rate  of 
reaction  between  chloracetic  acid  and  silver  nitrate,  represented 
by  the  equation 

CH2C1CO2H  +  AgNO3  +  H2O  =  CH2OHCO2H  +  AgCl  +  HNO3 
is  practically  the  same  in  water  and  in  45  per  cent,  alcohol. 

Influence  of  Temperature  on  the  Rate  of  Chemical 
Reaction — It  is  a  matter  of  common  experience  that  the  rate 
of  chemical  reactions  is  greatly  increased  by  rise  of  temperature. 
Thus  the  combination  of  hydrogen  and  oxygen  is  so  slow  at 
the  ordinary  temperature  that  it  cannot  be  detected  (p.  218), 
but  at  high  temperatures  it  proceeds  with  explosive  rapidity. 
It  has  already  been  pointed  out  that  rise  of  temperature  does 
not  usually  affect  the  form  of  the  velocity  equation ;  it  can  be 


226        OUTLINES  OF  PHYSICAL  CHEMISTRY 

represented  simply  as  altering  the  magnitude  of  the  velocity 
constant.  The  more  important  facts  in  this  connection  are  well 
illustrated  in  the  following  table,  which  represents  the  effect  of 
temperature  on  the  magnitude  of  the  velocity  constant  for  the 
unimolecular  reaction  between  dibromosuccinic  acid  and  water, 
represented  by  the  equation 

C2H2Br2(COOH)2  =  C2HBr(COOH)2  +  HBr. 

Temperature.         k  (time  in  minutes).  Temperature,  k  (time  in  minutes). 
15°                         0*00000967                70*1°  0*00169 

40°  •          0*0000863  80*0°  0*0046 

50°  0*000249  89*4°  0*0156 

60*2°  0*000654  101*0°  0*0318 

The  table  shows  (i)  that  the  velocity  increases  enormously 
with  rise  of  temperature  ;  at  15°  and  101°  the  relative  rates  are 
in  the  ratio  0*00000967:  0*0318  or  i  :  3300;  (2)  the  ratio 
for  a  rise  of  10°  is  approximately  the  same  at  different  tem- 
peratures, thus  /&8oA£7o  =  2'72>  ^50/^40  =  2*88.  It  is  import- 
ant to  remember  that  the  rate  of  most  chemical  reactions,  as 
in  the  above  example,  is  doubled  or  trebled  for  a  rise  of  10°. 
This  is  shown  in  the  accompanying  table,  which  gives  the  quo- 
tient for  10°  (kt+rfjkt)  for  a  few  typical  chemical  reactions.1 


1  The  third  column  contains  the  average  value  of  the  quotient  for  10°  be- 
tween the  temperatures  of  observation.  As  data  are  not  always  available 
at  intervals  of  10°,  the  average  value  of  kt+io°lkt  may  be  calculated  approxi- 
mately from  the  equation 

log10A2  -  log^  =  A  (Ta  -  Tj) 


where  *a  and  &2  are  the  velocity  constants  at  the  temperatures  Tl  and  T2 
respectively.  (See  next  section.)  This  equation  gives  us  the  value  of  A, 
and  the  quotient  for  10°  is  given  by 

Iog10(**+  io)/fo  =  IOA  or  *'+  ip  =  IOIOA 

R% 

As  an  example,  we  will  work  out  the  quotient  for  10°  for  the  inversion  of 
cane  sugar  from  the  data  given  in  the  table.  Log10  35-5  -  Iog10  0-765  is 
i  '66657  and  as  T2  -  Tj  =  30°  we  obtain  A  =  0-05555.  Hence  Iog10 
=  o*5555  and  (kt  +  10)/&  =  3-60  approximately. 


VELOCITY  OF  REACTION.     CATALYSIS          227 


Reaction. 


CH3COOC2H5  +  NaOH 
CH2ClCOONa  +  NaOH 
CH2ClCOONa  +  H2O   . 
C2H5ONa  +  CH3I 
Inversion  of  cane  sugar . 


Fermentation  by  yeast 


Velocity  Constants. 


=  2-307 
0*0008 


0-00336 
0*0120 

10-20° 
30-40° 


367  =  0*0034 


«M 

^30 
^55 


,=  21-648 
=  O-OI5 
=  0-OOI70 

2-I25 

35*5 


Quotient 
for  10°. 


1-23 
I-I7 
1-89 

3-2 

3*34 
3*6 

3*8 
1-6 


The  quotient  for  10°  for  reactions  in  solvents  other  than 
water  is  also  between  2  and  3  in  the  majority  of  cases. 

According  to  the  molecular  theory,  rise  of  temperature  ought  to 
increase  the  rate  of  chemical  change,  owing  to  the  accelerating 
effect  on  molecular  movements.  This  effect,  however,  would  only 
increase  proportionally  to  the  square  root  of  the  absolute  tempera- 
ture (p.  32),  and  it  can  easily  be  calculated  on  this  basis  that 
the  quotient  for  10°  for  a  bimolecular  reaction  at  the  ordinary 
temperature  would  be  about  1-04,  much  too  small  to  account 
for  the  large  temperature  coefficient  actually  observed.  Up  to 
the  present,  no  plausible  explanation  of  the  great  magnitude  of 
the  temperature  coefficient  of  chemical  reactions  has  been  given. 
The  only  other  property  which  appears  to  increase  as  rapidly 
with  temperature  is  the  vapour  pressure,  and  it  is  not  improbable 
that  there  is  a  close  connection  between  vapour  pressure  and 
chemical  reactivity. 

At  moderate  temperatures  the  temperature  coefficients  of 
enzyme  reactions  are  approximately  the  same  as  those  of 
chemical  reactions  in  general,  but  at  temperatures  in  the  neigh- 
bourhood of  o°,  the  rate  of  change  of  k  with  the  temperature 
is  often  abnormally  high,  as  the  table  shows. 

It  is  interesting  to  note  that  -the  rate  of  development  of 
organisms,  for  example,  the  rate  of  growth  of  yeast  cells,  the 
rate  of  germination  of  certain  seeds,  and  the  rate  of  develop- 


228       OUTLINES  OF  PHYSICAL  CHEMISTRY 

ment  of  the  eggs  of  fish,  is  also  doubled  or  trebled  for  a  rise 
of  temperature  of  10°,  and  it  has  therefore  been  suggested  that 
these  processes  are  mainly  chemical. 

Formulae  connecting  Reaction  Yelocity  and  Tempera- 
ture— As  has  already  been  pointed  out  (p.  167),  the  law  con- 
necting the  displacement  of  equilibrium  with  temperature  is 
known.  So  far,  however,  no  thoroughly  satisfactory  formula 
showing  the  relationship  of  rate  of  reaction  and  temperature 
has  been  established,  although  many  more  or  less  satisfactory 
empirical  formulae  have  been  suggested.  If  the  relationship 
which  has  been  shown  to  hold  approximately  for  the  rate  of  de- 
composition of  dibromosuccinic  acid — that  the  quotient  for  10° 
is  the  same  at  high  as  at  low  temperatures — holds  in  general, 
the  equation  connecting  k  and  T  must  be  of  the  form 

41og^)A*T      A 

where  A  is  constant.     On  integration,  this  becomes 
log£  =  AT  +  B, 

B  being  a  second  constant.  This  formula  holds  for  the  decom- 
position of  nitric  oxide  and  for  certain  other  reactions,  but  is 
not  generally  valid.  As  a  matter  of  fact,  the  quotient  kt+iJkt 
generally  diminishes  with  rise  of  temperature.  An  equation 
which  takes  account  of  this  has  been  proposed  by  Arrhenius ; 
in  its  integrated  form  the  equation  is  as  follows  : — 

log£  =  -  A/T  +  B. 

For  two  temperatures,  Tj  and  T2,  for  which  the  values  of  the 
velocity  constant  are  k±  and  k^  respectively,  the  above  equation 
becomes 


and  when  A  is  known  (from   two  observations)  the  velocity 
constant  for  any  other  temperature  can  be  calculated. 

Arrhenius  showed  that  the  above  empirical  equation  repre- 
sents satisfactorily  the  influence  of  temperature  on  the  rate  of 
hydrolysis  of  cane  sugar  and  on  certain  other  reactions,  and  it 


VELOCITY  OF  REACTION.     CATALYSIS      229 

has  since  been  employed  by  many  other  observers  with  fairly 
satisfactory  results.  A  is  a  constant  for  any  one  reaction,  but 
differs  for  different  reactions. 

Practical  Illustrations — As  the  rate  of  chemical  reactions 
alters  so  greatly  with  change  of  temperature,  it  is  necessary  in 
accurate  experiments  to  work  in  a  thermostat  provided  with  a 
regulator  to  keep  the  temperature  constant.  For  purposes  of 
illustration,  however,  sufficiently  accurate  results  can  be  obtained 
by  using  so  large  a  volume  of  solution  that  the  temperature 
does  not  alter  appreciably  during  the  reaction. 

Unimolecular  Reaction.  (a)  Decomposition  of  Hydrogen 
Peroxide 1 — To  200  c.c.  of  a  mixture  of  one  part  of  defibrinated 
ox-blood  and  10,000  parts  of  water,  an  equal  volume  of  about 
i/ioo  molar  hydrogen  peroxide  (0*34  grams  per  litre)  is  added, 
and  the  mixture  shaken.  At  first  every  ten  minutes,  and  then 
at  longer  intervals,  25  c.c.  of  the  reaction  mixture  is  removed 
with  a  pipette,  added  to  a  little  sulphuric  acid,  which  at  once 
stops  the  action,  and  titrated  with  i/ioo  normal  potassium 
permanganate.  If  pure  hydrogen  peroxide  is  not  available, 
the  commercial  product  should  be  neutralized  with  sodium 
hydroxide  before  use. 

Another  portion  of  the  original  hydrogen  peroxide  solution 
should  be  titrated  with  permanganate,  and  if  the  reacting 
solutions  have  been  measured  carefully,  the  initial  concentration 
in  the  reaction  mixture  may  be  taken  as  half  that  in  the  original 
solution. 

The  observations  should  be  calculated  by  substitution  in  the 
formula  i/t  log  a/a  -  x  =  0*4343  k,  valid  for  a  unimolecular 
reaction. 

A  corresponding  experiment  may  be  made  with  double  the 
peroxide  concentration,  in  order  to  illustrate  the  fact  that  the 
time  taken  to  complete  a  certain  fraction  of  the  reaction  is 
independent  of  the  initial  concentration. 

(b)  Hydrolytic  Decomposition  of  Cane  Sugar  in  the  Presence 
of  Acids — Equal  volumes  of  a  20  per  cent,  solution  of  cane 

1  Senter,  Zeitsch.  physikal.  Chem.,  1903,  44,  257.  The  amount  of  or- 
ganic matter  is  so  small  that  the  error  in  titration  due  to  its  reducing 
action  on  permanganate  is  negligible. 


23o       OUTLINES  OF  PHYSICAL  CHEMISTRY 

sugar  and  of  normal  hydrochloric  acid,  previously  warmed  to 
25°,  are  mixed,  the  observation  tube  of  a  polarimeter  is  filled 
with  the  mixture,  and  an  observation  of  the  rotation  taken  as 
quickly  as  possible.  The  polarimeter  tube  is  then  immersed 
in  a  thermostat  at  25°,  and  kept  in  the  latter  except  when 
readings  of  the  rotation  are  being  made.  In  order  that  it  may 
be  conveniently  immersed  in  a  thermostat,  the  polarimeter  tube 
is  provided  with  a  side  tube,  through  which  it  is  filled,  and  the 
end  of  which  is  not  immersed.  To  prevent  alterations  while 
readings  are  being  made,  the  tube  is  provided  with  a  jacket 
filled  with  water  at  the  temperature  of  the  thermostat. 

Several  chemists  have  described  arrangements  according  to 
which  the  tube  remains  in  the  polarimeter  throughout  an  ex- 
periment, the  temperature  being  kept  constant  by  passing  a 
stream  of  water  at  constant  temperature  through  the  jacket  of 
the  polarimeter  tube.1  With  rapid  working,  however,  the  simpler 
method  described  above  gives  excellent  results. 

If  it  is  convenient  to  make  an  observation  after  the  reaction 
is  complete  (say  24  hours),  the  total  change  of  reading  is  taken 
as  a  in  the  formula  for  a  unimolecular  reaction,  and  the  differ- 
ence of  the  initial  reading  and  that  at  the  time  /  is  proportional 
to  x,  the  amount  of  sugar  split  up.  If  the  reaction  is  not 
complete  in  a  reasonable  time,  the  final  reading  can  be  calculated 
from  the  fact  that  for  every  degree  of  rotation  to  the  right  in 
the  original  mixture,  the  wholly  inverted  mixture  will  rotate 
0-315°  to  the  left  at  25°. 

(c]  Hydrolysis  of  Ethyl  Acetate  in  the  Presence  of  Hydro- 
chloric Acid — The  method  of  experiment  in  this  case  has 
already  been  described  (p.  206). 

Bimolecular  Reaction,  (a)  The  rate  of  reaction  is  proportional 
to  the  concentration  of  each  of  the  reacting  substances — This  state- 
ment can  be  illustrated  very  satisfactorily  by  a  method  described 
by  Noyes  and  Blanchard,  and  depending  upon  the  fact  that 
the  time  taken  to  reach  a  certain  stage  of  a  reaction  is  inversely 
proportional  to  its  rate. 

1  C/.  Lowry,  Trans.  Faraday  Society,  1907,  3,  rig. 


VELOCITY  OF  REACTION.     CATALYSIS      231 

In  a  two-litre  flask  a  mixture  of  1600  c.c.  of  water,  50  c.c. 
half-normal  hydrochloric  acid  and  20-30  c.c.  of  dilute  mucilage 
of  starch  is  prepared,  and  400  c.c.  of  this  mixture  is  placed  in 
each  of  4  half-litre  flasks  of  clear  glass,  standing  on  white 
paper.  For  comparison,  a  fifth  half-litre  flask  contains  400 
c.c.  of  water,  10  c.c.  of  starch  solution,  and  sufficient  of  a  n/ioo 
solution  of  iodine  to  give  a  blue  colour  of  moderate  depth. 

Half-normal  solutions  of  potassium  bromate  (7  grams  per 
half-litre)  and  of  potassium  iodide  are  also  prepared.  To  the 
flasks  I.  and  II.  5  c.c.  of  the  bromate  solution  is  added,  and  to 
III.  and  IV.  10  c.c.  of  the  same  solution.  Then  at  a  definite 
time,  5  c.c.  of  the  iodide  solution  is  added  to  flask  I.,  the 
mixture  rapidly  shaken,  and  the  time  which  elapses  until  the 
solution  has  the  same  depth  as  the  test  solution  carefully  noted. 
Then  to  flasks  II.,  III.  and  IV.  are  added  successively  10  c.c., 
5  c.c.  and  10  c.c.  of  the  iodide  solution,  and  the  times  required 
to  attain  the  same  depth  of  colour  as  the  test  solution  carefully 
noted  in  each  case.  If  x  is  the  time  required  when  10  c.c.  of 
each  reagent  is  used,  2x  will  be  the  time  required  when  10  c.c. 
of  one  solution  and  5  c.c.  of  the  other  is  used,  and  4*  when 
5  c.c.  of  each  solution  is  used. 

If  for  some  reason  the  reactions  are  too  rapid,  the  strengths 
of  the  bromate  and  iodide  solutions  should  be  altered  till 
intervals  convenient  for  measurement  are  observed. 

(b)  Quantitative  measurement  of  a  bimolecular  reaction — The 
rate  of  reaction  between  ethyl  acetate  and  sodium  hydroxide  may 
be  measured  as  described  on  a  previous  page.  From  a  practical 
point  of  view,  however,  the  measurement  presents  certain  draw- 
backs because  it  is  difficult  to  prepare  a  solution  of  sodium  hy- 
droxide free  from  carbonate  and  also  to  prevent  absorption  of 
that  gas  from  the  air  during  the  experiment.  A  reaction J  free 
from  these  disadvantages,  which  is  very  rapid  in  dilute  solution, 
is  that  between  ethyl  bromoacetate  and  sodium  thiosulphate, 
represented  by  the  equation 
CH2BrCOOC2H5  +  Na2S2O3  =  CH2(NaS2O3)COOC2H5  +  NaBr. 

1  Slator,  Trans.  Chem.  Society,  1905,  87,  484. 


232       OUTLINES  OF  PHYSICAL  CHEMISTRY 

The  rate  of  the  reaction  can  readily  be  followed  by  removing  a 
portion  of  the  reaction  mixture  from  time  to  time  and  titrating 
with  n/ioo  iodine,  which  reacts  only  with  the  unaltered  thio- 
sulphate. 

300  c.c.  of  an  approximately  1/60  normal  solution  of  sodium 
thiosulphate  is  added  to  an  equal  volume  of  a  dilute  aqueous 
solution  of  ethyl  bromoacetate  (2-2-1  grams  per  litre)  in  a 
litre  flask,  the  mixture  shaken  and  the  flask  closed  by  a 
cork.  At  first  every  5  minutes,  and  then  every  10  or  15 
minutes,  50  c.c.  of  the  reaction  mixture  is  removed  with  a 
pipette  and  titrated  rapidly  with  n/ioo  iodine,  using  starch  as 
indicator.  Seven  or  eight  such  titrations  are  made,  and  then, 
after  an  interval  of  5-6  hours,  when  the  reaction  is  presumably 
complete,  a  final  titration  is  made  in  order  to  determine  the 
excess  of  thiosulphate  remaining.  The  initial  concentration  of 
thiosulphate,  expressed  in  c.c.  of  the  iodine  used  in  titrating 
the  mixture,  can  be  obtained  by  titrating  part  of  the  original 
thiosulphate  solution,  and  the  initial  concentration  of  bromo- 
acetate in  the  reaction-mixture  is  clearly  equivalent  to  the 
amount  of  thiosulphate  used  up.  The  case  is  exactly  analogous 
to  that  quoted  on  page  209,  in  which  the  sodium  hydroxide  is 
in  excess,  and  the  value  of  k  may  be  obtained  by  substitution 
in  equation  (3),  p.  208. 

Catalytic  Actions — The  decomposition  of  hydrogen  per- 
oxide by  blood  and  of  cane  sugar  in  the  presence  of  acids  are 
examples  of  catalytic  actions.  Hydrogen  peroxide  can  also  be 
decomposed  by  a  colloidal  solution  of  platinum,  which  may  be 
prepared  as  follows  (Bredig):  Two  thick  platinum  wires  dip 
into  ice-cold  water,  and  a  current  of  about  10  amperes  and 
40  volts  is  employed.  When  the  ends  of  the  wires  are  kept 
1-2  mm.  apart,  an  electric  arc  passes  between  them,  particles 
of  platinum  are  torn  off  and  remain  suspended  in  the  water. 
The  solution  is  allowed  to  stand  for  some  time,  and  filtered 
through  a  close  filter.  It  represents  a  dark-coloured  solution 
in  which  the  particles  cannot  be  detected  with  the  ordinary 


VELOCITY  OF  REACTION.     CATALYSIS      233 

microscope.  A  very  dilute  solution  may  be  used  to  decompose 
hydrogen  peroxide,  and  the  reaction  may  be  measured  as 
described  above  when  blood  is  employed. 

Catalytic  Action  of  Water — This  may  be  illustrated  by  its 
effect  on  the  combustion  of  carbon  monoxide  in  air,  which 
does  not  take  place  in  the  entire  absence  of  water  vapour. 
Carbon  monoxide  is  prepared  by  the  action  of  strong  sulphuric 
acid  on  sodium  formate  and  is  carefully  dried  by  passing 
through  two  wash-bottles  containing  strong  sulphuric  acid,  and 
finally  through  a  U  tube  containing  phosphorus  pentoxide. 
Some  time  before  the  experiment  is  to  be  tried,  a  little  strong 
sulphuric  acid  is  put  in  the  bottom  of  a  wide-mouthed  bottle 
with  a  close-fitting  glass  stopper,  and  the  bottle  allowed  to 
stand,  tightly  stoppered,  for  some  time. 

The  carbon  monoxide  issuing  from  the  apparatus  burns 
readily  in  air,  but  is  immediately  extinguished  if  the  wide- 
mouthed  bottle  is  placed  over  it.  If,  however,  a  small  drop  of 
water  is  placed  in  the  tube  whence  the  gas  is  issuing,  the  gas 
will  continue  to  burn  when  the  bottle  is  placed  over  it. 


CHAPTER  X 
ELECTRICAL  CONDUCTIVITY 

Electrical  Conductivity.  General — From  very  early  times 
it  was  noticed  that  electricity  can  be  conveyed  in  two  ways : 
(i)  In  conductors  of  the  first  class,  more  particularly  metals, 
without  transfer  of  matter ;  (2)  in  conductors  of  the  second 
class — salt  solutions  or  fused  salts — with  simultaneous  decom- 
position of  the  conductor.  We  are  here  concerned  only  with 
conductors  of  the  second  class,  but  the  use  of  the  terms  em- 
ployed in  electrochemistry  may  be  illustrated  by  reference  to 
conduction  in  metals. 

For  conductivity  in  general,  Ohm's  law  holds,  which  may  be 
enunciated  as  follows  :  The  strength  of  the  electric  current 
passing  through  a  conductor  is  proportional  to  tfie  difference 
of  potential  between  the  two  ends  of  the  conductor,  and  in- 
versely proportiotial  to  the  resistance  of  the  latter.  Strength 
of  current  is  usually  represented  by  C,  difference  of  potential 
or  electromotive  force  by  E,  and  resistance  by  R ;  Ohm's  law 
may  therefore  be  written  symbolically  as  follows  : — 

?-* 

The  practical  unit  of  electrical  resistance  is  the  ohm,  that  of 
electromotive  force  the  volt,  and  that  of  current  the  ampere. 
The  strength  of  an  electric  current  can  be  measured  in  various 
ways,  perhaps  most  conveniently  by  finding  the  weight  of  silver 
liberated  from  a  solution  of  silver  nitrate  in  a  de  finite  interval  of 
time.  An  ampere  is  that  strength  of  current  which  in  one 

234 


ELECTRICAL  CONDUCTIVITY  235 

second  will  deposit  0*001118  grams  of  silver  from  a  solution  of 
silver  nitrate  under  certain  definite  conditions.  Quantity  of  elec- 
tricity is  current  strength  x  time;  the  amount  of  electricity 
which  passes  in  one  second  with  a  current  strength  of  i  ampere 
is  a  coulomb.  When  there  is  a  difference  of  potential  of  one 
volt  between  two  ends  of  a  conductor,  and  a  current  of  i 
ampere  is  passing  through  it,  the  resistance  of  the  conductor 
is  i  ohm. 

The  resistance  of  a  metallic  conductor  is  proportional  to  its 
length  and  inversely  proportional  to  its  cross-section.  Hence 
if  /  is  the  length  and  s  the  cross  section,  the  resistance  R  is 

given  by  R  =  p  -,  where  p  is  a  constant  depending  only  on  the 

material  of  the  conductor,  the  temperature,  etc.,  and  is  termed 
the  specific  resistance.  If  both  /  and  s  are  equal  to  unity 
(i  cm.)  the  resistance  is  equal  to  p.  The  specific  resistance,  p, 
of  a  conductor  is  therefore  the  resistance  in  ohms  which  a  cm. 
cube  of  it  offers  to  the  passage  of  electricity.  If  there  is  a 
difference  of  potential  of  i  volt  between  two  sides  of  the  cube, 
and  the  current  which  passes  is  i  ampere,  the  specific  resistance 
of  the  cube  is,  by  Ohm's  law,  =  i.  A  conductor  of  low  resist- 
ance is  said  to  have  a  high  electrical  conductivity,  that  is,  it 
readily  allows  electricity  to  pass.  Conductivity  is  therefore  the 
converse  of  resistance,  and  specific  conductivity ',  K  =  i//o,  where 
p  is  specific  resistance.  Specific  conductivity  is  measured  in 
reciprocal  ohms,  sometimes  termed  mhos.  In  order  to  illustrate 
the  magnitude  of  these  factors,  the  specific  resistance  and  the 
specific  conductivity  of  a  few  typical  substances  at  18°  are  given 
in  the  table  : — 

30  per  cent. 
Substance.  Silver.  Copper.       Mercury.    Gas  carbon,    sulphuric 

acid. 

Sp.  resistance,  p         0-0000016    0-0000017    0*00009      0-0050          0-74 
Sp.  conductivity,  K       624,000        587,000       10,240          200  1-35 

Silver  has  the  highest  conductivity  of  all  known  substances , 


236       OUTLINES  OF  PHYSICAL  CHEMISTRY 

gas  carbon  is  a  comparatively  poor  conductor;  and  30  per 
cent,  sulphuric  acid,  one  of  the  best  conducting  solutions,  is 
enormously  inferior  to  the  metals  in  this  respect. 

Electrolysis  of  Solutions.  Faraday's  Laws— We  now 
consider  the  phenomena  accompanying  the  conduction  of 
electricity  in  aqueous  solutions  of  salts.  If,  for  example,  two 
platinum  plates,  one  connected  to  the  positive,  the  other  to  the 
negative  pole  of  a  battery,  are  dipped  into  a  solution  of  sodium 
sulphate,  it  will  be  observed  that  hydrogen  is  immediately  given 
off  at  the  plate  connected  to  the  negative  pole  of  the  battery, 
and  oxygen  at  the  plate  connected  to  the  positive  pole. 
Further,  if  a  few  drops  of  litmus  have  previously  been  added 
to  the  solution,  it  will  be  noticed  that  the  solution  round  the 
positive  plate  or  pole  becomes  red,  indicating  the  production 
of  acid,  and  that  round  the  negative  pole  becomes  blue,  showing 
the  formation  of  alkali.  An  ammeter  placed  in  the  circuit  will 
show  that  a  current  is  passing  through  the  solution,  so  that  the 
chemical  changes  in  question  accompany  the  passage  of  the 
current.  Even  if  the  poles  are  far  apart,  the  gases  are  liberated, 
and  the  acid  and  alkali  appear  immediately  connection  is  made 
through  the  solution,  and  if  the  current  is  continued,  the  acid 
and  alkali  accumulate  round  the  respective  poles  without  any 
apparent  change  in  the  main  bulk  of  liquid  between  the  poles. 
These  phenomena  can  scarcely  be  accounted  for  otherwise  than 
*by  supposing  that  matter  travels  with  the  current,  and  that  part 
travels  towards  the  positive  pole  and  part  towards  the  negative 
pole.  To  these  travelling  parts  of  the  solution  Faraday  gave 
the  name  of  ions. 

It  will  be  well  to  mention  here  the  nomenclature  used  in 
this  part  of  the  subject.  A  solution  or  fused  salt  which  con- 
ducts the  electric  current  is  termed  an  electrolyte.  The  plate 
in  the  solution  connected  to  the  positive  pole  of  the  battery 
is  termed  the  positive  pole,  positive  electrode  or  anode,  that 
connected  to  the  negative  pole  of  the  battery  the  negative 
pole,  negative  electrode  or  cathode.  The  ions  which  move 


ELECTRICAL  CONDUCTIVITY  237 

towards  the  anode  are  often  termed  anions,  those  travelling 
towards  the  cathode  cations. 

We  will  now  consider  the  relationship  between  the  amount 
of  chemical  action  and  the  quantity  of  electricity  passed  through 
a  solution.  The  amount  of  chemical  action  might  be  estimated 
by  measuring  the  volume  of  gas  liberated  at  one  of  the  poles, 
or  by  the  amount  of  metal  deposited  on  an  electrode.  This 
question  was  investigated  by  Faraday,  and  as  a  result  he 
established  a  law  which  bears  his  name,  and  which  may  be 
enunciated  as  follows  :  For  the  same  electrolyte,  the  amount  of 
chemical  action  is  proportional  to  the  quantity  of  electricity  which 
passes.1  Further,  Faraday  measured  the  relative  quantities  of 
substances  liberated  from  different  solutions  by  the  same  quantity 
of  electricity,  and  was  thus  led  to  the  discovery  of  his  so-called 
second  law  :  The  quantities  of  substances  liberated  at  the  elec- 
trodes when  the  same  quantity  of  electricity  is  passed  through 
different  solutions  are  proportional  to  their  chemical  equivalents. 
The  chemical  equivalent  of  any  element  (or  group  of  elements) 
is  equal  to  the  atomic  weight  (or  sum  of  the  atomic  weights) 
divided  by  the  valency.  The  second  law,  therefore,  states  that 
if  the  same  quantity  of  electricity  is  passed  through  solutions  of 
sodium  sulphate,  cuprous  chloride,  cupric  sulphate,  silver 
nitrate  and  auric  chloride,  the  relative  amounts  of  hydrogen 
and  the  metals  liberated  are  as  follows  :  — 
Electrolyte  Na2SO4  CuCl  CuSO4  AgNO3  AuCl3 


z  ;  0=  f  ,  A.  S»,  CV=  5^;  Ag  .  2",  A..2Z 

The  above  result  may  also  be  expressed  rather  differently  as 
follows  :  The  electrochemical  equivalents  (the  proportions  of 
different  elements  set  free  by  the  same  current)  are  proportional 
to  the  chemical  equivalents. 

That  quantity  of  electricity  which  passes  through  an  electro- 
lyte when  the  chemical  equivalent  of  an  element  (or  group  of 

1  Faraday  measured  the  amount  of  electricity  by  its  action  on  a  mag- 
netic needle. 


238        OUTLINES  OF  PHYSICAL  CHEMISTRY 

elements)  in  grams  is  being  liberated  will  obviously  be  a 
quantity  of  very  considerable  importance  in  electrochemistry. 
Since  i  ampere  in  i  second  (a  coulomb)  liberates  0*00001036 
grams  of  hydrogen,  it  follows  that  when  the  chemical  equivalent 
of  hydrogen  or  any  other  element  is  liberated,  i/o '0000103 6 
=  96540  coulombs  must  pass  through  the  electrolyte.  It 
is  often  designated  by  the  symbol  F  (faraday).  One  cou- 
lomb will  liberate  35-45  x  0-00001036  =  0*000368  grams  of 
chlorine,  127  x  o'ooooio36  =  o§ooi3i6  grams  of  iodine,  and 
1 08  x  0*00001036  =  o'ooi  1 1 8  grams  of  silver. 

Mechanism  of  Electrical  Conductivity — It  has  already 
been  pointed  out  (p.  236)  that  during  the  electrolysis  of  sodium 
sulphate  the  products  of  electrolysis  appear  only  at  the  poles, 
the  main  bulk  of  solution  between  the  poles  being  apparently 
unaffected.  This  is  most  readily  accounted  for  on  the  view 
that  part  of  the  solute  is  moving  towards  the  positive  and  part 
towards  the  negative  pole,  these  moving  parts  being  termed 
anions  and  cations  respectively.  We  now  assume  further  that 
the  cations  are  charged  with  positive  electricity,  and  move 
towards  the  negatively  charged  cathode  owing  to  electrical 
attraction ;  similarly,  the  negatively  charged  anions  are  attracted 
to  the  cathode.  When  the  ions  reach  the  poles,  they  give  up 
their  charges,  which  neutralize  a  corresponding  amount  of  the 
opposite  kinds  of  electricity  on  the  anode  and  cathode  respec- 
tively, and  then  appear  as  the  elements  or  compounds  we  are 
familiar  with.  The  process  of  electrolysis  is  illustrated  in  Fig. 
29.  Into  the  vessel  containing  sodium  sulphate  solution  dip 
two  electrodes  (on  opposite  sides  of  the  vessel)  connected  with 
the  positive  and  negative  poles  of  the  battery  respectively.  The 
direction  of  motion  of  the  ions  to  the  oppositely-charged  poles 
is  illustrated  by  the  arrows. 

It  is  not  always  an  easy  matter  to  say  what  the  moving 
ions  are.  It  is  only  rarely  that  they  are  set  free  as  such,  since 
secondary  reactions  often  take  place  at  the  electrodes.  When 
a  strong  solution  of  cupric  chloride  is  electrolysed,  copper 


ELECTRICAL  CONDUCTIVITY 


239 


and  chlorine  are  liberated  at  the  cathode  and  anode  respectively, 
and  it  is  probable  that  these  substances  are  the  ions.  In  the 
case  of  sodium  sulphate,  however,  for  which  hydrogen  and 
oxygen  are  the  products  of  electrolysis,  secondary  reactions 
must  take  place.  The  current  is  in  all  probability  conveyed 
through  the  solution  by  Na  and  SO4  ions.  When  the  former 
reach  the  cathode,  they  give  up  their  charges  and  form  metallic 
sodium,  which  immediately  reacts  with  the  water,  forming  sodium 
hydroxide  and  hydrogen.  In  the  same  way  the  SO4  ions,  on 
reaching  the  anode,  give  up  their  charges,  and  the  free  SO4 
group  then  reacts  with  the  water  according  to  the  equation 
SO4  +  H2O  =  H2SO4  +  O,  oxygen  being  liberated  and  sul- 
phuric acid  regener- 
ated. In  this  way 
the  phenomena  al- 
ready described  are 
readily  accounted 
for. 

So  far,  we  have 
assumed  that  the 
material  of  the  elec- 
trodes is  not  acted 
on  by  the  products 
of  electrolysis.  This 
is  generally  true 
when  the  electrodes 
are  made  of  platinum 
or  other  resistant  FIG.  29. 

metal,  but  in   other 

cases  secondary  reactions  take  place  between  the  discharged 
ions  and  the  poles.  Thus  when  a  solution  of  copper  sulphate 
is  electrolysed  between  copper  poles,  the  SO4  ions,  after  losing 
their  charges,  react  with  the  anode  according  to  the  equation 
Cu  +  SO4  =  CuSO4,  so  that  the  net  result  of  the  electrolysis 
of  copper  sulphate  between  copper  poles  is  the  transfer  of  copper 
from  the  anode  to  the  cathode. 


24o        OUTLINES  OF  PHYSICAL  CHEMISTRY 

We  have  assumed  that  in  a  solution  of  sodium  sulphate  the 
moving  ions  are  Na  and  SO4.  As  the  Na  ion  moves  towards 

the  negative  electrode,  it  must  already  be  positively  charged  ; 

+ 
this  may  be  indicated  thus  :  Na  (Fig.  29),  or,  more  concisely, 

by  a  dot,  thus :  Na\  As  neither  positive  nor  negative  elec- 
tricity accumulates  in  the  solution  during  electrolysis,  the 
amount  of  positive  electricity  neutralized  on  the  anode  must 
be  equivalent  to  that  neutralized  on  the  cathode.  Hence,  since 
two  sodium  ions  are  discharged  for  every  SO4  ion,  the  latter 
must  carry  double  the  amount  of  electricity  that  a  sodium 
ion  carries,  and  this  is  indicated  by  the  symbols  SO4  or  SO4" 
(Fig.  29). 

According  to  our  present  views,  the  metallic  components  of 
salts  in  solution  are  positively  charged,  the  number  of  charges 
corresponding  with  the  ordinary  valencies  of  the  metals.  Some 
important  cations  are  K*,  Na-,  Ag-,  NH4-,  Ca",  Hg2",  Hg", 
Fe",  Fe1",  etc.  The  remainder  of  the  salt  molecule  constitutes 
the  negative  ion,  which,  like  the  positive  ion,  may  have  one,  two 
or  more  (negative)  electric  charges.  Among  the  more  important 
anions  are  Cl',  Br',  I',  NO3',  SO4",  CO3",  PO4'",  etc.  Acids  and 
bases  deserve  special  consideration  from  this  point  of  view. 
Since  salts  are  derived  from  acids  by  replacing  the  hydrogen  by 
metals,  it  is  natural  to  suppose  that  the  positive  ion  in  aqueous 
solutions  of  acids  is  H',  and  that  the  remainder  of  the  molecule 
constitutes  the  negative  ion.  On  the  other  hand,  aqueous  solu- 
tions of  all  bases  contain  the  OH'  group.  These  points  are 
dealt  with  fully  at  a  later  stage. 

Freedom  of  the  Ions  before  Electrolysis — The  fact  that 
the  ions  begin  to  move  towards  the  respective  electrodes  im- 
mediately the  current  is  made  appears  to  indicate  that  they  are 
electrically  charged  in  the  solution  before  electrolysis  is  com- 
menced. The  questions  therefore  arise  as  to  the  state  of  such 
a  salt  as  sodium  chloride  in  dilute  solution,  and  as  to  what 
occurs  when  the  circuit  is  completed.  The  view  long  held  was 
that  the  atoms  are  united  to  form  a  molecule,  NaCl,  at  least 


ELECTRICAL  CONDUCTIVITY  241 

partly  owing  to  the  electrical  attraction  of  their  contrary  Charges, 
and  that  the  current  pulls  them  apart  during  electrolysis.  Careful 
measurements  show,  however,  that  Ohm's  law  holds  for  electro- 
lytes, from  which  it  follows  that  the  electrical  energy  expended  in 
electrolysis  is  entirely  used  up  in  overcoming  the  resistance  of  the 
electrolyte,  so  that  no  work  is  done  in  pulling  apart  the  components 
of  the  molecule.  On  the  basis  of  this  observation,  and  in  agree- 
ment with  certain  views  previously  enunciated  by  Williamson  as  to 
the  kinetic  nature  of  equilibrium  in  general  (cf.  p.  160),  Clausius 
showed  that  the  equilibrium  condition  in  electrolytes  cannot  be 
such  that  the  ions  of  contrary  charge  are  firmly  bound  together ; 
on  the  contrary,  the  equilibrium  must  be  of  a  kinetic  nature,  so 
that  the  ions  are  continuously  exchanging  partners,  and  must, 
at  least  momentarily,  be  present  in  solution  as  free  ions.  The 
average  fraction  of  the  ions  free  under  definite  conditions  of 
temperature  and  dilution  was  not  estimated  by  Clausius,  but  he 
considered  that  the  fraction  was  probably  very  small.  Clausius's 
theory  accounts  for  the  qualitative  phenomena  of  electrolysis, 
as  during  their  free  intervals  the  ions  would  be  progressing 
towards  the  oppositely  charged  poles,  and  would  finally  reach 
them  and  be  discharged. 

The  views  of  Clausius  were  further  developed  in  1887  by 
Arrhenius^who  first  showed  how  the  fraction  of  the  molecules 
split  up  into  ions  could  be  deduced  from  electrical  conduc- 
tivity measurements,  and  independently  from  osmotic  pressure 
measurements.  This  constitutes  the  main  feature  of  the  theory 
of  electrolytic  dissociation,  which  is  dealt  with  in  detail  later 
(p.  260),  and  the  fact  that  the  two  methods  for  determining 
the  fraction  of  the  molecules  present  as  free  ions  gave  results 
in  very  satisfactory  agreement  contributed  much  to  the  general 
acceptance  of  the  theory.  In  a  normal  solution  of  sodium  chlo- 
ride, then,  there  is  an  equilibrium  between  free  ions  and  non- 
ionised  molecules,  represented  by  the  equation  NaCl  ^±  Na-  +  Cl', 
in  which,  according  to  Arrhenius,  about  70  per  cent,  of  the 
salt  is  ionised  and  the  remaining  30  per  cent,  is  present  as 

1  Zeltsch.  physikal.  Chem.,  1887,  i,  631. 
16 


242         OUTLINES  OF  PHYSICAL  CHEMISTRY 

NaCl  molecules.  According  to  this  theory,  the  electrical  con- 
ductivity is  determined  exclusively  by  the  free  ions,  and  not  at 
all  by  the  non-ionised  molecules  or  by  the  solvent. 

Dependence  of  the  Conductivity  on  the  Number  and 
Nature  of  the  Ions — We  are  now  in  a  position  to  form  a 
picture  of  the  mechanism  of  electrical  conductivity  in  a  solu- 
tion. Suppose  there  are  two  parallel  electrodes  i  cm.  apart 
(Fig.  29)  with  the  electrolyte  between  them,  and  that  the  differ- 
ence of  potential  between  the  electrodes  is  kept  constant,  say 
at  i  volt.  Before  the  electrodes  are  connected  with  the  battery, 
the  ions  are  moving  about  in  all  directions  through  the  solution. 
When  connection  is  made — in  other  words,  when  the  electrodes 
are  charged — they  exert  a  directive  force  on  the  charged  ions, 
which  move  towards  the  poles  with  the  contrary  charges. 
Those  nearest  the  poles  arrive  first,  give  up  their  charges  to 
the  poles,  thus  neutralising  an  equivalent  amount  of  electricity 
on  the  latter,  and  then  either  appear  in  the  ordinary  uncharged 
form  (e.g.,  copper),  react  with  the  solvent  (e.g.,  SO4  when  platinum 
electrodes  are  used),  with  the  electrodes  (e.g.,  SO4  with  copper 
electrodes),  or  with  each  other.  It  will  be  seen  that  the  process 
does  not  consist  in  the  direct  neutralisation  of  the  electricity  on 
the  positive  electrode  by  that  on  the  negative  electrode,  but 
part  of  the  charge  on  the  anode  is  neutralised  by  the  anions, 
whilst  an  equivalent  amount  of  charge  on  the  cathode  is 
neutralised  by  the  cations — a  process  which  has  the  same 
ultimate  effect  as  direct  neutralisation. 

On  this  basis  it  is  clear  that  with  a  constant  E.M.F.  the  rate 
at  which  the  charges  on  our  two  plates  are  neutralised,  in  other 
words,  the  conductivity  of  the  solution  between  them,  depends 
on  three  things :  (i)  the  number  of  carriers  or  ions  per  unit 
volume ;  (2)  the  load  or  charge  which  they  carry ;  (3)  the  rate 
at  which  they  move  to  the  electrodes.  Each  of  these  factors 
will  now  be  briefly  considered. 

(i)  The  Number  of  Ions — Other  things  being  equal,  the 
conductivity  of  a  solution  will  clearly  be  proportional  to  the 


ELECTRICAL  CONDUCTIVITY  243 

number  of  ions  per  unit  volume.  For  the  same  electrolyte, 
the  number  of  ions  can,  of  course,  be  varied  by  varying  the 
concentration  of  the  solution.  In  general,  it  may  be  said  that 
on  increasing  of  concentration  the  ionic  concentration  also  in- 
creases, but  the  exact  relationship  will  be  dealt  with  later.  For 
different  electrolytes  of  the  same  equivalent  concentration,  the 
conductivity  will  depend  on  the  extent  to  which  the  solute  is 
split  up  into  its  ions  and  on  their  speed. 

(2)  The  Charge  Carried  by  the  Ions — As  has  already  been 
pointed  out,  there  is  a  simple  relationship  between  the  capacity 
of  different  ions   for  transporting  electricity,  since  the  gram- 
equivalent  of  any  ion   (positive  or   negative)  conveys  96,540 
coulombs.     Thus  if  in  an  hour  (  =  3600  seconds)  a  gram-equiva- 
lent of  sodium  (23  grams)  and  of  chlorine  (35*47  grams)  are 
discharged  at  the  respective  electrodes,  the  current  which  has 
passed  through  the  cell  is 

96'*4°  =  26-8  amperes. 
3600 

(3)  Migration  Velocity  of  the  Ions — In  this  section  we 
will  for  simplicity  consider  only  univalent  ions,  but  the  same 
considerations   apply  to   all    electrolytes.     Since  positive  and 
negative  ions  are  necessarily  discharged  in  equivalent  amount 
(p.  240),  and  the  number  of  positive  and  negative  univalent  ions 
discharged  in  a  given    time   is   therefore    equal,  it  might  be 
supposed  that  the  ions  must  travel  at  the  same  rate.     This, 
however,  is  by  no   means  the  case.     Our  knowledge  of  this 
subject  is  mainly  due  to  Hittorf,  who  showed  that  the  relative 
speeds  of  the  ions  could  be  deduced  from  the  changes  in  concen- 
tration round  the  electrodes  after  electrolysis. 

The  effect  of  the  unequal  speeds  of  the  ions  on  the  concen- 
trations round  the  poles  is  made  clear  by  the  accompanying 
scheme  (Fig.  30),  a  modified  form  of  one  given  by  Ostwald. 
The  vertical  dark  lines  represent  the  anode  and  cathode  respec- 
tively, and  the  dotted  lines  divide  the  cell  into  three  sections, 
those  in  contact  with  the  electrodes  being  termed  the  anode 


244       OUTLINES  OF  PHYSICAL  CHEMISTRY 


and  cathode  compartments  respectively.  The  positive  ions  are 
represented  by  the  usual  +  sign,  and  the  negative  ions  by  the 
—  sign.  I.  represents  the  state  of  affairs  in  the  solution  before 
connection  is  made ;  the  number  of  anions  is  the  same  as  that 
of  the  cations,  and  the  concentration  is  uniform  throughout. 
The  remaining  lines  represent  the  state  of  affairs  in  the  solution 
after  electrolysis  on  different  assumptions  as  to  the  relative 


I. 


nr. 


u. 


f  *  +  + 

-f-   +   4-    t    +   + 

4-    f    +    -f- 

4-    -1-  rh    4- 

+    +   -1-    +   +  + 

+    +  4   4- 

4-    4- 

4-   4-  4-  4-   4-  4- 

f   4-    f  -f  -f   + 

4- 

4-    4-  +    f  4-  + 

f   f   -f    •)•   +   f  + 

FIG.  30. 


speeds  of  the  ions.  Suppose  at  first  that  only  the  negative 
ions  move.  The  condition  of  affairs  in  the  solution  when  all 
the  negative  ions  have  moved  two  steps  to  the  left  is  shown  in 
II.  Each  ion  left  without  a  partner  is  supposed  to  be  dis- 
charged, and  the  figure  shows  that  although  the  positive  ions 
have  not  moved  an  equal  number  of  positive  ions  is  discharged. 
Further,  whilst  the  concentration  in  the  anode  compartment 
has  not  altered  during  the  electrolysis,  the  concentration  in  the 
cathode  compartment  has  been  reduced  by  half. 

Suppose  now  that  the  positive  and  negative  ions  move  at  the 
same  rate.     The  state   of  affairs  when  each  ion,  positive  or 


ELECTRICAL  CONDUCTIVITY  245 

negative,  has  moved  two  steps  towards  the  oppositely-charged 
pole  is  represented  in  III.  It  is  evident  that  four  positive  and 
four  negative  ions  have  been  discharged,  and  that  the  con- 
centration of  undecomposed  salt  has  diminished  in  both  com- 
partments, and  to  the  same  extent,  namely  by  two  molecules. 

Finally,  let  us  assume  that  both  ions  move,  but  at  unequal 
rates,  so  that  the  positive  ions  move  faster  than  the  negative  ions 
in  the  ratio  3:2.  The  state  of  affairs  when  the  positive  ions 
have  moved  three  steps  to  the  right,  and  the  negative  ions  two 
steps  to  the  left,  is  shown  in  IV.  It  is  clear  that  five  positive 
and  five  negative  ions  have  been  discharged,  and  that  whilst 
there  is  a  fall  of  concentration  of  two  molecules  round  the 
cathode,  there  is  a  fall  of  three  round  the  anode. 

These  results  show  that  the  fall  of  concentration  round  any 
one  of  the  electrodes  is  proportional  to  the  speed  of  the  ion 
leaving  it.  In  II.,  for  example,  there  is  a  fall  of  concentration 
round  the  cathode,  but  not  round  the  anode,  corresponding 
with  the  fact  that  the  anion  moves,  but  not  the  cation. 
Similarly,  in  III.,  the  fall  of  concentration  round  anode  and 
cathode  is  equal,  corresponding  with  the  fact  that  the  anion 
and  cation  move  at  the  same.  Finally,  in  IV.,  fall  round 
anode  :  fall  round  cathode  :  :  3  :  2,  corresponding  with  the  fact 
that  speed  of  cation  :  speed  of  anion  =  3:2.  From  these 
examples  we  obtain  the  important  rule  that 

Fall  of  concentration  round  anode     _  speed  of  cation 
Fall  of  concentration  round  cathode      speed  of  anion 

The  student  often  finds  a  difficulty  in  understanding  how,  as  in 
IV.,  five  ions  can  be  discharged  at  the  anode  when  only  two 
anions  have  crossed  the  partitions.  To  account  for  this,  it 
must  be  assumed  that  there  is  always  an  excess  of  ions  in 
contact  with  the  electrodes,  so  that  more  are  discharged  than 
actually  arrive  by  diffusion. 

The  speed  of  the  cations  is  often  represented  by  u,  and  that 
of  the  anions  by  v.  The  total  quantity  of  electricity  (say,  unit 


246        OUTLINES  OF  PHYSICAL  CHEMISTRY 


quantity)  carried  is  proportional  to  (u  +  v),  and,  of  this  total 
n  =  vl(u  +  v)  is  carried  by  the  anions  and  i  -  n  =  u/(u  +  v) 
by  the  cations,  n,  the  fraction  of  the  current  carried  by  the 
anion,  is  termed  the  transport  number  of  the  anion ;  similarly, 
i  -  n  is  the  transport  number  of  the  cation. 

It  is  evident  from  the  figure  that  there  is  a  central  section  of 
the  cell  between  the  dotted  lines  in  which  no  change  of  con- 
centration takes  place  when  elec- 
trolysis is  not  carried  too  far. 
Therefore,  in  order  to  investigate 
the  changes  in  concentration,  it  is 
simply  necessary  to  remove  the 
solutions  round  the  electrodes 
after  electrolysis  and  analyse 
them,  but  the  experiment  will  only 
be  successful  if  the  intermediate 
layer  has  not  altered  in  strength, 

Practical  Determination  of 
the  Relative  Migration  Velo- 
cities of  the  Ions — The  experi- 
ment may  conveniently  be  made 
in  the  modified  form  of  Hittorfs 
apparatus  used  in  Ostwald's  labo- 
ratory (Fig.  31).  It  consists  of 
two  glass  tubes  communicating 
towards  the  upper  ends  ;  one  of 
them  is  closed  at  the  lower  end, 
and  the  other  provided  with  a 
stopcock,  as  shown.  The  elec- 
trodes, A  and  K,  are  sealed  into 
FIG.  31.  glass  tubes  which  pass  up  through 

the    liquid,    and    communication 

with  a  battery  is  made  in  the  usual  way  by  means  of  wires  which 
pass  down  the  interior  of  the  glass  tubes. 

As  an  illustration,  the  determination  of  the  transport  numbers 


ELECTRICAL  CONDUCTIVITY  247 

of  the  Ag'  and  NO3'  ions  in  a  solution  of  silver  nitrate  will  be 
described.  The  anode  A  is  of  silver,  and  should  be  covered  with 
finely-divided  silver  by  electrolysis  just  before  the  experiment ; 
the  cathode  is  of  copper.  The  electrodes  are  placed  in  position, 
the  anode  compartment  filled  up  to  the  connecting  tube  with  1/20 
normal  silver  nitrate,  the  cathode  compartment  up  to  B  with  a 
concentrated  solution  of  copper  nitrate,  and  finally  the  apparatus 
is  carefully  filled  up  with  the  silver  nitrate  solution  in  such  a  way 
that  the  boundary  between  the  two  solutions  at  B  remains  fairly 
sharp.  The  cell  is  then  connected  in  series  with  a  high  adjust- 
able resistance,  an  ammeter,  and  a  silver  voltameter,  and  then 
joined  to  the  terminals  of  a  continuous  current  lighting  circuit 
(no  volts)  in  such  a  way  that  the  silver  pole  becomes  the 
anode.  By  means  of  the  variable  resistance,  the  current  is  so 
adjusted  that  a  current  of  about  o'oi  ampere  is  obtained  (to  be 
read  off  on  the  ammeter),  and  the  electrolysis  continued  for 
about  two  hours.  Finally,  a  measured  amount  (about  3/4)  of 
the  anode  solution  is  run  off  and  titrated  with  thiocyanate  in 
the  usual  way.  The  strength  of  the  current  can  be  read  off 
on  the  ammeter,  and  from  this  and  the  time  during  which 
the  current  has  passed,  the  total  quantity  of  electricity  passed 
through  the  solution  can  be  calculated.  It  is,  however,  prefer- 
able to  employ  for  this  purpose  the  silver  voltameter  above 
referred  to.  It  consists  of  a  tube  with  stopcock  similar  to  the 
left-hand  part  of  the  transport  apparatus  (Fig.  31),  and  is 
provided  with  a  silver  electrode  (to  serve  as  anode)  similar  to 
that  in  the  other  apparatus,  and  placed  in  a  corresponding 
position  (in  the  lower  part  of  the  tube).  The  tube  is  filled  to 
3/4  of  its  length  with  a  15-20  per  cent,  solution  of  sodium  or 
potassium  nitrate,  and  carefully  filled  up  with  dilute  nitric  acid 
so  that  the  two  solutions  do  not  mix.  The  cathode,  of  platinum 
foil,  dips  in  the  nitric  acid.  During  electrolysis,  the  NO3'  ions 
dissolve  silver  from  the  anode,  and  by  titrating  the  whole  of  the 
contents  with  ammonium  thiocyanate  after  the  experiment,  the 
amount  of  silver  in  solution  can  be  determined,  and  from  this 


248        OUTLINES  OF  PHYSICAL  CHEMISTRY 

the  quantity  of  electricity  which  has  passed  through  the  solution 
can  readily  be  calculated  (p.  238). 

We  now  return  to  the  transport  apparatus.  For  our  purpose 
it  will  be  sufficient  to  deal  only  with  the  change  of  concentra- 
tion in  the  anode  compartment.  From  this  the  transport 
number  of  the  cation  is  obtained,  and  the  transport  number 
of  the  anion  is  then  at  once  obtained  by  difference.  During 
electrolysis,  the  silver  concentration  round  the  anode  diminishes 
owing  to  migration  of  silver  ions  towards  the  cathode.  The 
process  may  conveniently  be  illustrated  by  III.  of  Fig.  30  where 
the  fall  owing  to  migration  is  from  4  to  2.  At  the  same  time, 
however,  NO3  ions  reach  the  anode,  and  after  being  discharged 
dissolve  silver  from  it,  the  silver  concentration  in  the  anode 
compartment  therefore  increasing.  The  latter  effect  is  the 
same  as  that  taking  place  simultaneously  in  the  silver  volta- 
meter, as  described  above,  and  therefore,  if  no  silver  migrated 
from  the  anode,  the  total  increase  of  concentration  in  this  com- 
partment would  be  equal  to  that  in  the  silver  voltameter, 
which,  as  explained  above,  is  a  measure  of  the  total  quantity 
of  electricity  which  passes ;  we  will  term  this  a.  If  b  is  the 
(unknown)  change  in  concentration  due  to  the  migration  of 
the  silver  ions,  the  observed  change  in  concentration  at  the 
anode  will  be  a  —  b.  As  a  is  known,  and  a  —  b  is  found  by 
titrating  the  anode  solution  after  the  experiment,  b  can  readily 
be  obtained. 

In  practice,  the  greater  part  of  the  anode  solution  after 
electrolysis  is  run  into  a  beaker,  it  is  then  weighed  or  an  aliquot 
part  measured,  and  titrated. 

The  calculation  of  the  results  will  be  rendered  clear  from  the 
details  of  an  experiment  made  in  Ostwald's  laboratory.  Before 
the  experiment  12-31  grams  of  the  silver  nitrate  solution  re- 
quired 26-56  c.c.  of  a  1/50  n  potassium  thiocyanate  solution, 
so  that  i  gram  of  solution  contained  0*00739  grams  of  silver 
nitrate.  After  the  experiment,  23-38  grams  of  the  anode 
solution  required  69-47  c.c.  of  the  thiocyanate  solution,  cor- 


ELECTRICAL  CONDUCTIVITY  249 

responding  to  0-2361  grams  of  silver  nitrate.  The  solution, 
therefore,  contained  23  -14  grams  of  water,  which  before  the 
experiment  contained  23-14  x  0*00739  =  0-1710  grams  of 
silver  nitrate,  hence  the  increase  of  concentration  at  the  anode 
is  0*0651  grams  =  a  -  b.  The  contents  of  the  silver  volta- 
meter required  36*16  c.c.  of  thiocyanate  =  0*1229  grams  of 
silver  nitrate  =  a  ;  the  same  amount  is  dissolved  at  the  anode 
in  the  transport  apparatus.  As  the  actual  increase  of  con- 
centration was  only  0*0651  grams,  0*1229  -  0*0651  =  0*0578 
grams  of  silver  must  have  left  the  anode  compartment  by  migra- 
tion. Hence  the  transport  number  for  silver  is 


u 

!  _    n  =  -  =  _        _  —  0*470, 
u  +  v      0*1229 

and  for  the  NO3'  ion 

v          0*06151 

n  =  -  =  --  —  =  0*530. 
u  +  v       0-1229 

Hence,  of  the  total  current  47  per  cent,  is  carried  by  the  silver 
ions,  and  53  per  cent,  by  the  NO3'  ions. 

It  was  shown  by  Hittorf  that  the  transport  numbers  are 
practically  independent  of  the  E.M.F.  between  the  electrodes, 
but  depend  to  some  extent  on  the  concentration  and  on  the 
temperature.  It  is  remarkable  that  at  higher  temperatures 
they  tend  to  become  equal.  Some  of  the  numbers  are  given 
in  the  next  section. 

Specific,  Molecular  and  Equivalent  Conductivity  —  Just 
as  in  the  case  of  metallic  conduction,  the  resistance  of  an  electro- 
lyte is  proportional  to  the  length,  and  inversely  proportional  to 
the  cross-section  of  the  column  between  the  electrodes.  Hence 
we  may  define  the  specific  resistance  of  an  electrolyte  as  the 
resistance  in  ohms  of  a'  cm.  cube,  and  its  specific  conductivity 
as  i  /specific  resistance,  expressed  in  reciprocal  ohms.  Since, 
however,  the  conductivity  does  not  depend  on  the  solvent  but 
on  the  solute,  it  is  much  more  convenient  to  deal  with  solutions 
containing  quantities  of  solute  proportional  to  the  respective 
molecular  weights.  The  so-called  molecular  conductivity,  /x,  is 


250       OUTLINES  OF  PHYSICAL  CHEMISTRY 

most  largely  used  in  this  connection ;  it  is  the  conductivity,  in 
reciprocal  ohms,  of  a  solution  containing  i  mol  of  the  solute 
when  placed  between  electrodes  exactly  i  cm.  apart.  It  may 
also  be  defined  as  the  specific  conductivity,  /c,  of  a  solution, 
multiplied  by  v,  the  volume  in  c.c.  which  contain  a  mol  of  the 
solute.  Hence  we  have 

fJL    =    KV. 

As  an  example,  the  following  values  for  the  specific  and  mole- 
cular conductivities  of  solutions  of  sodium  chloride  at  18°,  as 
given  by  Kohlrausch,  may  be  quoted. 

Sp.  Con-  Molecular 

Concentration  of  Solution.  ductivity,        Conductivity, 

K.  KV. 

ro        molar  (v=  1,000)  0*0744  74-4 

0*1         molar  (v=  10,000)  0*00925  92*5 

o'oi       molar  (v=  100,000)  0*001028  102*8 

o'ooi     molar  (v=  1,000,000)  0*0001078  107*8 

0*0001  molar  (v=  10,000,000)  0*00001097  109*7 

It  will  be  noticed  that  the  molecular  conductivity  as  defined 
above  increases  at  first  with  dilution,  but  beyond  a  certain 
point  remains  practically  constant  on  further  dilution. 

These  numbers  enable  us  to  illustrate  more  fully  the  physical 
meaning  of  the  molecular  conductivity.  Imagine  a  cell  of  i  cm. 
cross-section  and  of  unlimited  height,  two  opposite  walls  through- 
out the  whole  height  acting  as  electrodes.  If  a  litre  of  a 
molar  solution  of  sodium  chloride  is  placed  in  the  cell,  it  will 
stand  at  a  height  of  1000  cms.  We  may  regard  the  solution 
as  made  up  of  cm.  cubes,  1000  in  number,  and  if  the  con- 
ductivity of  one  of  these  cubes — the  specific  conductivity — is 
Klf  the  total  conductivity  (in  other  words  the  molecular  con- 
ductivity) is  loooKj.  If  now  another  litre  of  water  is  added,  the 
height  of  the  solution  will  be  2000  cms.  and  its  molecular  con- 
ductivity is  now  2ooo*2,  where  *2  is  the  specific  conductivity  of 
the  half-molar  solution.  In  exactly  the  same  way,  the  mole- 
cular conductivity  may  be  determined  at  still  greater  dilutions. 
From  the  above  it  is  clear  that  a  measure  of  the  conducting 


ELECTRICAL  CONDUCTIVITY  251 

power  of  a  mol  of  the  electrolyte  in  different  dilutions  is  ob- 
tained by  multiplying  the  volume  in  c.cs.  in  which  the  electrolyte 
is  dissolved  by  its  specific  conductivity  at  that  dilution,  or  in 
symbols 

/x  =  KV 
as  given  above. 

A  glance  at  the  last  two  lines  in  the  table  helps  us  to  under- 
stand the  approximately  constant  value  of  p  in  very  dilute 
solutions.  When  the  solution  is  diluted  from  i/iooo  to 
1/10,000  molar,  the  specific  conductivity  is  reduced  to  about 
i/io,  but  as  the  volume  is  ten  times  as  great,  the  molecular 
conductivity  is  only  slightly  altered. 

Besides  the  molecular  conductivity,  the  term  equivalent  con- 
diictivity  is  sometimes  used.  As  the  name  implies,  it  is  the 
specific  conductivity  of  a  solution  multiplied  by  the  volume 
in  c.c.  which  contains  a  gram-equivalent  of  the  solute. 

Kohlrausch's  Law.  Ionic  Velocities — The  numbers  in 
the  third  column  of  the  above  table  show  that  the  molecular 
conductivity  of  sodium  chloride  increases,  at  first  rapidly  and 
then  very  slowly,  with  dilution.  This  subject  was  investigated 
for  a  number  of  solutions  by  Kohlrausch,  who  found  that  for 
solutions  of  electrolytes  of  high  conductivity  (salts,  so-called 
"  strong  "  acids  and  bases)  the  molecular  conductivity  increases 
with  dilution  up  to  about  i/ioooo  molar  solution,  and  beyond 
that  point  remains  practically  constant  on  further  dilution. 
Kohlrausch  showed  further  that  this  limiting  value  of  the  mole- 
cular conductivity,  which  may  be  represented  by  p^,  is  different 
for  different  salts,  and  may  be  regarded  as  the  sum  of  two  inde- 
pendent factors — one  pertaining  to  the  cation  or  positive  part 
of  the  molecule,  the  other  to  the  anion,  or  negative  part  of  the 
molecule.  This  experimental  result  is  termed  Kohlrausch's  law, 
and  is  readily  intelligible  on  the  basis  of  the  theory  of  electrical 
conductivity  developed  above.  The  limiting  value  of  the  mole- 
cular conductivity  is  reached  when  the  molecule  is  completely 
split  up  into  its  ions ;  under  these  circumstances  the  whole  of 
the  salt  takes  part  in  conveying  the  current.  For  simplicity  we 
will  consider  solutions  of  binary  electrolytes.  In  very  dilute 


252       OUTLINES  OF  PHYSICAL  CHEMISTRY 

equimolar  solutions  of  different  electrolytes,  the  number  of  the 
ions  and  their  charges  are  the  same,  and  the  observed  differences 
of  /X.QC  can  only  be  due  to  the  different  speeds  of  the  ions.  The 
limiting  molecular  conductivities  of  binary  electrolytes  are 
therefore  proportional  to  the  sum  of  the  speeds  of  the  ions, 
and  when  the  units  are  properly  chosen  we  have 

/AOC  =  u  +  v, 

where  u  is  the  speed  of  the  cation,  v  that  of  the  anion.  This  is 
the  mathematical  form  of  Kohlrausch's  law,  and  expresses  the 
very  important  result  that  in  sufficiently  dilute  solution  the  speed 
of  an  ion  is  independent  of  the  other  ion  present  in  solution. 

From  the  results  of  conductivity  measurements,  only  the 
sum  of  the  speeds  of  the  ions  can  be  deduced,  but,  as  has 
already  been  shown,  the  relative  values  iof  u  and  v  can  be 
obtained  from  the  results  of  migration  experiments  (p.  246). 
It  was  found  by  Kohlrausch  that  the  value  of  yu,^  =  u  +  v 
for  silver  nitrate  at  18°  is  H5'5.  The  accurate  value  for  the 
transport  number  of  the  anion,  NO3',  is  n  —  vj(u-  +  v}  =  0-518. 
Hence  v  =  0*518  x  115*5  —  6o'8  and  u  =  0-482  x  1.15*5  — 
557.  The  values  of  u  and  vt  expressed  in  these  units,  are 
termed  the  ionic  velocities,  under  the  conditions  of  the  experi- 
ment. The  accompanying  table  gives  the  ionic  velocities, 
calculated  from  the  results  of  conductivity  and  transport  measure- 
ments, for  some  of  the  more  common  ions  in  infinite  dilution *  at 
1 8°,  expressed  in  the  same  units  as  the  molecular  conductivity 
of  sodium  chloride  (p.  250): — 

H-    =  318  Li-       =  36  OH'  =  174 

K-    =    65  NH4-  =  64  Cl'     =    66 

Na-  =    45  Ag-     =56  I'       ==    67 

NO3'=    6 1 

It  is  interesting  to  observe  that  the  velocity  of  the  H-  ion  is 
relatively  very  high,  about  five  times  as  great  as  that  of  any  of  the 
metallic  ions.  The  ion  which  comes  next  to  it  is  the  OH'  ion,, 

1  The  more  concentrated  the  solution,  the  smaller  are  the  ionic  velocities, 
owing  to  the  increased  resistance  to  their  motion. 


ELECTRICAL   CONDUCTIVITY  253 

the  speed  of  which  is  more  than  half  that  of  the  H-  ion,  and 
much  greater  than  that  of  any  of  the  other  ions.  Since  the 
conductivity  of  a  solution  is,  as  we  have  already  seen,  propor- 
tional to  the  speed  of  the  ions,  it  follows  that  the  solutions  of 
highly  ionised  acids  and  bases  will  have  a  relatively  high  con- 
ductivity. Thus,  under  conditions  otherwise  equal  as  regards 
concentration,  ionisation,  temperature,  etc.,  the  conductivities 
of  dilute  solutions  of  hydrochloric  acid  and  of  sodium  chloride 
will  be  iii  the  ratio  (318  4-  66)  =  384  to  (45  +  66)  =  in,  or 
about  3-5:1. 

Absolute  Velocity  of  the  Ions.  Internal  Friction— 
The  absolute  velocity  of  the  ions  is  proportional  to  the  E.M.F. 
between  the  electrodes,  and  inversely  proportional  to  the  re- 
sistance offered  to  their  passage  by  the  solvent.  When  the 
fall  of  potential  is  one  volt  per  cm.  (i.e.,  when  the  difference  of 
potential  between  the  electrodes  is  x  volts  and  the  distance 
between  them  is  x  cm.)  it  can  be  shown  that  the  absolute 
velocities,  in  cm.  per  second,  are  obtainable  from  the  values 
for  the  ionic  velocities  given  above  by  dividing  by  96,540 
or,  what  is  the  same  thing,  by  multiplying  by  1-036  x  io~5. 
Hence  the  absolute  velocity  of  the  hydrogen  ion  is,  under  the 
conditions  described,  318  x  1-036  x  io~5  =  0*00332  cm.  per 
second,  and  of  the  potassium  ion  0-00067  cm-  Per  second  at 
infinite  dilution.  The  speed  of  the  ions  is  therefore  extremely 
low ;  even  the  hydrogen  ions,  under  a  driving  force  of  i  volt 
per  cm.,  only  move  about  twice  as  fast  as  the  extremity  of  the 
minute  hand  of  an  ordinary  watch.  This  very  slow  motion 
of  the  moving  particles  indicates  that  the  resistance  to  their 
passage  through  the  solvent  is  very  great.  Kohlrausch  has 
calculated  that  the  force  required  to  drive  a  gram  of  sodium 
ions  through  a  solution  at  the  rate  of  i  cm.  per  second  is 
153  x  io6  kilograms  weight,  or  about  150,000  tons  weight. 

The  absolute  velocity  of  the  ions  can  also  be  measured 
directly  by  a  method  the  principle  of  which  is  due  to  Lodge, 
and  which  may  be  illustrated  by  an  experiment  described  by 


254       OUTLINES  OF  PHYSICAL  CHEMISTRY 

Danneel.  A  U-tube  is  partly  filled  with  dilute  nitric  acid, 
and  in  the  lowest  part  of  the  tube  a  solution  of  potassium 
permanganate,  the  specific  gravity  of  which  has  been  increased 
as  much  as  possible  by  the  addition  of  urea,  is  carefully  placed, 
by  means  of  a  pipette,  in  such  a  way  that  the  boundary  between 
the  acid  and  the  permanganate  remains  sharp.  When  platinum 
electrodes  are  dipped  in  the  nitric  acid  in  the  two  limbs,  and 
a  current  passed  through  the  solution,  the  violet  boundary  (due 
to  the  coloured  MnO4'  ion)  moves  towards  the  anode.  From 
the  observed  speed  of  the  boundary  and  the  difference  of 
potential  between  the  poles,  the  speed  of  the  ion  for  a  fall 
of  potential  of  i  volt/cm,  is  obtained,  and  has  been  found  to 
agree  exactly  with  the  value  obtained  by  conductivity  and 
transport  measurements. 

This  method  is  not  confined  to  salts  with  coloured  ions,  but 
the  moving  boundary  can  also  be  observed  with  colourless 
solutions  when,  as  is  usually  the  case,  the  refractive  index  of 
the  two  solutions  is  different.  There  are,  of  course,  two 
boundaries,  one  due  to  the  positive  ions  moving  towards  the 
cathode,  and  the  other  due  to  the  negative  ions  moving  towards 
the  anode.  When  the  conditions  are  such  that  both  can  be 
observed,  the  relative  speeds  give  the  ratio  u/v  directly. 

Measurements  of  ionic  velocities  on  this  principle  have  been 
made  by  Masson,  Steele  and  others,  and  the  results  are  in 
entire  agreement  with  those  obtained  indirectly. 

Experimental  Determination  of  Conductivity  of  Elec- 
trolytes— The  measurement  of  the  conductivity  of  conductors 
of  the  first  class  is  a  very  simple  operation.  Until  compara- 
tively recently,  however,  no  very  satisfactory  results  for  the 
conductivity  of  electrolytes  could  be  obtained,  because  when 
a  steady  current  is  passed  through  a  solution  between  platinum 
electrodes  the  products  of  electrolysis  accumulate  at  the  poles 
and  set  up  a  back  E.M.F.  of  uncertain  value,  a  phenomenon 
known  as  polarization  (p.  373).  This  difficulty  is,  however,  com- 
pletely got  over  by  using  an  alternating  instead  of  a  direct 


ELECTRICAL  CONDUCTIVITY 


255 


current  (Kohlrausch,  1880)  ;  by  the  rapid  reversal  of  the  current 
the  two  electrodes  are  kept  in  exactly  the  same  condition,  and 
there  is  no  polarization. 

The  arrangement  of  the  apparatus,  which  in  principle  amounts 
to  the  measurement  of  resistance  by  the  Wheatstone  bridge 
method,  is  shown  in  Fig.  32.  R  is  a  resistance  box,  S  a  cell 
with  platinum  electrodes,  between  which  is  the  solution  the 
resistance  of  which  is  to  be  measured,  ab  is  a  platinum  wire 
of  uniform  thickness,  which  may  conveniently  be  a  metre  long, 
and  is  stretched  along  a  board  graduated  in  millimetres,  c  is 
a  sliding  contact.  By  means  of  a  battery  (not  shown  in  the 
figure)  a  direct 
current  is  sent 
through  a  Ruhm- 
korff  coil,  K,  the 
latter  then  gives 
rise  to  an  alter- 
nating current, 
which  divides  at 
a  into  two 
branches,  reach- 
ing b  by  the  paths 
adb  and  acb  re- 
spectively. As  a  galvanometer  is  not  affected  by  an  alter- 
nating current,  it  is  in  this  case  replaced  by  a  telephone  T, 
which  is  silent  when  the  points  c  and  d  are  at  the  same  potential. 
The  contact-maker,  c,  is  shifted  along  the  wire  till  the  telephone 
no  longer  sounds.  Under  these  circumstances,  the  following 
relationship  holds  — 

Length  of  ac      Length  of  cb 


FIG.  32. 


and  since  ac,  cb  and  R  are  known,  S,  the  resistance  of  the  part 
of  the  electrolyte  between  the  electrodes,  can  et  once  be 
calculated. 

As  the  resistance  of  electrolytes  varies   within  wide  limits, 


256       OUTLINES  OF  PHYSICAL  CHEMISTRY 

different  forms  of  cell  are  employed  according  to  circum- 
stances. For  solutions  of  small  conductivity,  the  Arrhenius 
form  represented  in  Fig.  33.  is  very  suitable.  The  electrodes, 
which  are  stout  platinum  discs  2-4  cm.  in  diameter,  are  fixed 
(by  welding  or  otherwise)  to  platinum  wires,  which  are  sealed 
into  glass  tubes  A  and  B,  as  shown  in  the  figure.  These  glass 
tubes  are  fixed  firmly  into  the  ebonite  cover  of  the  cell,  so  that 


FIG.  33. 


FIG.  34. 


the  distance  between  the  electrodes  remains  constant,  and  electri- 
cal connection  is  made  in  the  usual  way  by  wires  passing  down  the 
interior  of  the  glass  tubes.  In  order  to  expose  a  larger  surface, 
and  thus  minimise  polarization  effects,  which  would  interfere 
with  the  sharpness  of  the  minimum  in  the  telephone,  the  elec- 
trodes are  coated  with  finely-divided  platinum  by  electrolysis 
of  a  solution  of  chlorplatinic  acid.  For  electrolytes  of  high 


ELECTRICAL   CONDUCTIVITY  257 

conductivity,  a  modified  form  of  conductivity  vessel,  with 
smaller  electrodes  placed  further  apart,  has  been  found  con- 
venient (Fig.  34). 

Experimental  Determination  of  Molecular  Conduc- 
tivity —  It  is  clear  that  the  observed  resistance  of  the  electro- 
lyte must  depend  on  what  is  usually  termed  the  capacity  of  the 
cell,  that  is,  on  the  cross-section  of  the  electrodes  and  the 
distance  between  them.  The  specific  conductivity,  and  hence 
the  specific  resistance,  of  the  electrolyte  could  be  calculated  if 
these  two  magnitudes  were  known  (p.  235);  but  it  is  much 
simpler  to  determine  the  "  constant  "  of  the  vessel,  which  is 
proportional  to  its  capacity,  by  using  an  electrolyte  of  known 
conductivity.  For  this  purpose,  a  1/50  molar  solution  of  potas- 
sium chloride  may  conveniently  be  used  for  cells  of  the  first 
type.  The  method  of  procedure  will  be  clear  from  an  example. 
Referring  to  the  figure,  we  have,  for  the  resistance,  S,  of  the 
electrolytic  cell 


,  .  .  i         ac 

and  conductivity  C  =  =•  =  =r-r- 
ac  S      R'&r 

Further,  since  the  specific  conductivity,  K,  must  be  proportional 
to  the  observed  conductivity,  we  have 


where  A  is  a  constant.  Since  all  the  other  factors,  including  K, 
the  specific  conductivity  of  potassium  chloride,  are  known,  A, 
the  constant  of  the  cell,  can  be  calculated.  If,  now,  with  the 
same  distance  between  the  electrodes,  a  solution  of  unknown 
specific  conductivity,  KV  is  put  in  the  cell,  and  for  the  resistance 
R'  the  new  position  of  the  contact  is  c\  the  specific  conductiv- 
ity in  question  is  given  by  the  formula 

ac 

«i  =  ARW- 

By  multiplying  KX  by  the  number  of  c.c.  containing  i  mol  of  the 
solute,  the  molecular  conductivity  is  obtained. 
17 


258        OUTLINES  OF  PHYSICAL  CHEMISTRY 

From  the  results  of  conductivity  measurements  in  different 
dilutions,  /A^  can  readily  be  obtained  directly  for  salts,  strong 
acids  and  bases ;  it  is  the  value  to  which  /x,  approximates  on 
progressive  dilution,  p^  cannot,  however,  be  obtained  directly 
for  weak  electrolytes,  such  as  acetic  acid  and  ammonia ;  before 
the  limiting  value  of  the  conductivity  is  reached  with  these 
electrolytes,  the  solutions  would  be  so  dilute  as  to  render  accu- 
rate measurement  of  the  specific  conductivity  impossible.  This 
difficulty  is  got  over  by  making  use  of  Kohlrausch's  law.  The 
value  of  ftoo  for  acetic  acid  must  be  the  sum  of  the  velocities 
of  the  H*  and  CH3COO'  ions.  The  former  is  obtained  from  the 
results  of  conductivity  and  transport  measurements  with  any 
strong  acid,  and  has  the  value  318  at  1 8°.  In  a  similar  way 
the  velocity  of  the  CH3COO'  ion  can  be  obtained  from  ob- 
servations with  an  acetate  for  which  the  value  of  p^  can  con- 
veniently be  found,  e.g.,  sodium  acetate.  JJL^  for  the  latter  salt  at 
1 8°  is  78* i,  and  as  the  velocity  of  the  Na*  ion  is  44*4  at  infinite 
dilution,  that  of  the  CH3COO'  ion  must  be  78-1  -44-4  =  33-7. 
Hence  for  acetic  acid 

/*oo  =  »  +  v  =  337  +  318  =  3517  at  1 8°. 

Results  of  Conductivity  Measurements — In  general,  it 
may  be  said  that  the  conductivity  of  pure  liquids  is  bmall. 
Thus  the  specific  conductivity  of  fairly  pure  distilled  water  is 
about  io~6  reciprocal  ohms  at  18°,  and  even  this  small  con- 
ductivity is  largely  due  to  traces  of  impurities.  It  is  a  remark- 
able fact  that  the  specific  conductivity  of  a  number  of  other 
liquids,  which  have  been  purified  very  carefully  by  Walden,1  is 
of  the  same  order  as  that  given  above  for  water. 

Mixtures  of  two  liquids  have  in  many  cases  a  very  small 
conductivity,  not  appreciably  greater  than  that  of  the  pure 
liquids  themselves ;  this  is  true  of  mixtures  of  glycerine  and 
water,  and  of  alcohol  and  water.  On  the  other  hand,  a 
mixture  of  two  liquids  which  are  practically  non-conductors 
may  have  a  very  high  conductivity — for  example,  mixtures  of 
sulphuric  acid  and  water.  The  results  obtained  for  this  mix- 
1  Zeitsch.  Physikal  Ghent.,  1903,  46,  103. 


ELECTRICAL  CONDUCTIVITY 


259 


ture  are  represented  in  Fig.  35,  the  acid  concentration  being 
measured  along  the  horizontal  axis,  and  the  specific  conductivity 
along  the  vertical  axis.  The  figure  shows  that,  on  gradually 
adding  sulphuric  acid  to  water,  the  specific  conductivity  of  the 
mixture  increases  till  30  per  cent,  of  acid  is  present,  reaches  a 
maximum  value  at  that  point,  and  on  further  addition  of  acid 
diminishes.  When  pure  sulphuric  acid  is  present  (100  per  cent, 
on  curve),  the  conductivity  is  practically  zero,  and  is  increased 


07 


0-6 


0-4 


0-3 


\ 


Concentration 


V 


10        20         30 


40       50      60       70       80      90      ioo  per  cent. 
FIG.  35. 


both  by  the  addition  of  water  (left-hand  part  of  curve)  and  of 
sulphur  trioxide  (right-hand  part  of  curve).  Further,  the  curve 
has  a  minimum  between  84  and  85  per  cent,  of  acid,  which,  it 
is  interesting  to  note,  exactly  corresponds  with  the  composition 
of  the  mono  hydrate  H2SO4,  H2O.  According  to  the  electro- 
lytic dissociation  theory,  the  conductivity  depends  on  the  pres- 
ence of  free  ions,  and  the  curve  for  sulphuric  acid  and  water 
shows  in  a  very  striking  way  that  the  condition  most  favourable 
for  ionisation  is  the  presence  of  two  substances.  Why  ions  are 
formed  in  a  mixture  of  sulphuric  acid  and  water,  and  not 
appreciably,  if  at  all,  in  a  mixture  of  alcohol  and  water,  is  not 
well  understood  (cf.  p.  317). 

Analogous  phenomena  are  met  with  for  solutions  of  solids 


26o        OUTLINES  OF  PHYSICAL  CHEMISTRY 

and  of  other  liquids  in  liquids.  An  aqueous  solution  of 
sugar  has  no  appreciable  conducting  power.  The  so-called 
"  strong  "  acids  and  bases  form  well-conducting  liquids  with 
water.  The  conductivity  of  most  organic  acids  and  bases  is 
small,  and  in  corresponding  dilution  ammonium  hydroxide  is 
a  much  poorer  conductor  than  potassium  hydroxide.  On  the 
other  hand,  all  salts,  even  the  salts  of  organic  acids  which  are 
themselves  weak,  have  a  very  high  conductivity. 

The  conductivity  of  substances  in  solvents  other  than  water 
is  usually  small,  but  solutions  in  methyl  and  ethyl  alcohols  and 
in  liquid  ammonia  are  exceptions.  The  dependence  of  electrical 
conductivity  on  the  nature  of  the  solvent  will  be  discussed  later 

It  is  interesting  to  note  that  many  fused  salts,  such  as  silver 
nitrate  and  lithium  chloride,  are  good  conductors,  and  thus  form 
an  exception  to  the  rule  that  pure  substances  belonging  to  the 
second  class  of  conductors  have  a  very  small  conductivity. 

Electrolytic  Dissociation — It  has  already  been  pointed 
out  (p.  124)  that  solutions  of  salts,  strong  acids  and  bases,  have 
a  much  higher  osmotic  pressure  in  aqueous  solution  than  would 
be  the  case  if  Avogadro's  hypothesis  was  valid  for  these  solu- 
tions. According  to  the  molecular  theory,  the  solutions  behave 
as  if  there  were  more  particles  of  solute  present  than  would  be 
anticipated  from  the  simple  molecular  formula,  and  van't  Hoff 
expressed  this  by  a  factor  /,  which  represented  the  ratio  between 
the  observed  and  calculated  osmotic  pressures.  This  was  the 
position  of  the  theory  of  solution  in  1885. 

About  that  time,  Arrhenius  pointed  out  that  there  is  a  close 
connection  between  electrical  conductivity  and  abnormally  high 
osmotic  pressures  ;  only  those  solutions  which,  according  to  van't 
Hoff 's  theory,  have  abnormally  high  osmotic  pressures,  conduct 
the  electric  current.  Kohlrausch  had  previously  shown  that  the 
molecular  conductivity  increases  at  first  with  dilution,  and  for 
many  electrolytes  attains  a  limiting  value  in  a  dilution  of 
10,000  litres  (p.  251).  Arrhenius  accounted  for  this  increase 
on  the  assumption  that  the  solute  consists  of  "active"  and 


ELECTRICAL   CONDUCTIVITY  261 

"  inactive  "  parts,  and  that  only  the  active  parts,  the  ions,  convey 
the  current.  The  extent  to  which  the  solute  is  split  up  into 
ions  increases  with  the  dilution  until  finally  (when  the  molecular 
conductivity  has  attained  its  maximum  value)  it  is  completely 
ionised  or  completely  "  active  "  as  far  as  the  conduction  of 
electricity  is  concerned. 

The  theory  of  Arrhenius  is  based  upon  the  views  of  Clausius 
on  conductivity,  as  has  already  been  pointed  out.  Arrhenius, 
however,  went  much  further,  inasmuch  as  he  showed  how,  from 
the  results  of  conductivity  and  of  osmotic  pressure  measure- 
ments, the  degree  of  dissociation  can  be  calculated,  as  shown  in 
the  following  section. 

Degree  of  lonisation  from  Conductivity  and  Osmotic 
Pressure  Measurements  —  According  to  the  theory  of  electro- 
lytic dissociation,  the  conductivity  of  a  solution  depends  only  on 
the  number  of  the  ions  per  unit  volume,  on  their  charges  (which 
are  the  same  for  equivalent  amounts  of  different  electrolytes) 
and  on  their  speed.  For  the  same  electrolyte  we  may  assume 
that  the  velocities  remain  practically  unaltered  on  dilution  (the 
friction  in  a  dilute  solution  being  practically  the  same  as  that 
in  pure  water),  therefore  the  increase  of  molecular  conductivity 
with  dilution  must  depend  almost  entirely  on  an  increase  in 
the  number  of  the  ions.  The  molecular  conductivity  at  infinite 
dilution  is  given  by  the  formula 

^  =  u  +  v, 

where  u  and  v  are  the  speeds  of  cation  and  anion  respectively 
and  the  molecular  conductivity  at  any  dilution,  v,  must  therefore 
be  represented  by  the  formula 

Pv  =  a(u  +  v), 

where  a  represents  the  fraction  of  the  molecules  split  up  into 
ions.  Hence,  dividing  the  second  equation  by  the  first,  we 
have 


Moo 


262        OUTLINES  OF  PHYSICAL  CHEMISTRY 

that  is,  the  degree  of  dissociation,  a,  at  any  dilution,  is  the 
ratio  of  the  molecular  conductivity  at  that  dilution  to  the  mole- 
cular conductivity  at  infinite  dilution.  For  example,  /j,v  for  molar 
sodiurn  chloride  is  74*3  and  p^  =  110*3,  hence  a  =  yu,u//xoc  = 
74'3/iio'3  =  0-673.  Hence  sodium  chloride  in  molar  solution 
is  about  two-thirds  split  up  into  its  ions. 

We  have  now  to  consider  the  deduction  of  the  degree  of 
dissociation  from  osmotic  measurements.  The  assumption  made 
in  this  case  is  that  the  osmotic  pressure  is  proportional  to  the 
number  of  particles  present,  the  ions  acting  as  separate  entities. 
If  a  molecule  is  partially  dissociated  into  n  ions  and  the  degree 
of  dissociation — the  ionised  fraction — is  a,  then  the  number  of 
molecules  will  be  i  -  a,  and  the  number  of  ions  no..  Hence 
the  ratio  of  the  number  of  particles  actually  present  to  that 
deduced  according  to  Avogadro's  hypothesis  (van't  Hoffs  factor 
/)  will  be 

/'=i  —  a+«a=i+  a(n  -   i), 
i  —  i 


or  a 


n  -  i 


As  an  illustration,  de  Vries  obtained  for  a  0*14  molar  solution 
of  potassium  chloride  /=  i'8i,  hence,  since  n  =  2,  a  =  o'8i, 
or  the  salt  is  dissociated  to  the  extent  of  8 1  per  cent,  into  its 
ions,  /for  a  o'i8  molar  solution  of  calcium  nitrate  is  2-48, 

1-48 
therefore,  since  «  =  3,  a  =•  -   -  =  074  in  this  case. 

The  agreement  in  the  values  of  /  obtained  from  conductivity 
and  osmotic  measurements  is  strikingly  shown  in  the  accom- 
panying table  (van't  Hoff  and  Reicher,  1889).  The  values  of 
i  (osmotic)  are  from  the  results  of  de  Vries,  those  of  /  (freezing 
point)  mainly  from  the  observations  of  Arrhenius,  and  those 
of  /  (conductivity)  are  calculated  by  means  of  the  formulae 
a  =  /AU//XOC  and  i  =  i  +  a(n  -  i)  as  explained  above. 


Concentration 
(gram  equiv. 
per  litre). 

i  (freezing 
pt.). 

i  (osmotic). 

i  (conduc- 
tivity). 

0*14 

1*82 

1*81 

1*86 

0*13 

i  '94 

1*92 

1*84 

0-18 

2'47 

2-48 

2*46 

0*19 

2*68 

2*79 

2/48 

0*184 

2*67 

2-78 

2*42 

ELECTRICAL  CONDUCTIVITY  263 

Substance. 

KC1 
LiCl 

Ca(N03)2 

MgQ2 

CaCl2 

The  agreement  is  satisfactory,  and  goes  far  to  justify  the  as- 
sumptions on  which  the  data  have  been  calculated.  It  is  not 
certain  that  the  results  obtained  by  the  different  methods  can 
be  expected  to  agree  absolutely  ;  this  point  will  be  referred  to  at 
a  later  stage  (p.  281). 

As  regards  the  mode  of  ionisation,  it  is  clear  that  univalent 
compounds,  such  as  potassium  chloride,  can  ionise  only  in  one 
way,  thus,  KCl^K*  +  Cl'.  For  more  complex  molecules,  how- 
ever, there  are  other  possibilities,  thus  calcium  chloride  may 
ionise  as  follows:  CaQ2^CaCl-  +  Cl'  as  well  as  in  the  normal 
way  CaCl2^±Ca**  +  2C1'.  If  ionisation  were  complete  according 
to  the  last  equation,  /  would  be  =  3,  as  compared  with  the 
observed  value,  2*67  for  0-184  normal  solution,  given  in  the 
table.  Similarly,  sulphuric  acid  may  dissociate  according  to 
the  equation  H2SO42H'  +  HSO4',  the  latter  ion  then  under- 
going further  ionisation  as  follows :  HSO/^tH*  +  SO4". 

Effect  of  Temperature  on  Conductivity — The  conduc- 
tivity of  electrolytes  increases  considerably  with  rise  of  tempera- 
ture. The  temperature  coefficient  for  salts  is  0*020  to  0*023, 
for  acids  and  some  acid  salts  0*009  to  0*016,  for  caustic  alkalis 
about  0-020,. and  does  not  vary  much  with  dilution.  Conduc- 
tivity data  are  usually  given  for  18°,  and  the  specific  conductivity, 
K,  at  any  other  temperature,  is  given  by  the  formula 

Kt  =  Kl8[i  +  C(t  -  18)] 
where  c  is  the  temperature  coefficient. 

As  the  conductivity  of  an  electrolyte  depends  both  on  the 
number  and  velocity  of  the  ions,  the  question  arises  as  to 
whether  the  change  of  conductivity  with  temperature  is  due 
to  the  alteration  of  only  one  or  of  both  these  factors.  The 


264       OUTLINES  OF  PHYSICAL  CHEMISTRY 

matter  can  be  at  once  decided  by  calculating  the  degree  of 
dissociation  at  the  higher  temperature  from  conductivity 
measurements  in  the  ordinary  way,  and  comparing  with  that 
at  the  lower  temperature.  For  normal  sodium  chloride  at 
50°,  the  value  of  a  =  /AB//AOC  =  132/203*5  =  0*65,  which  is 
only  slightly  less  than  the  value  at  18°,  0-678.  Hence,  as  the 
considerable  increase  of  conductivity  with  temperature  cannot 
be  due  to  an  increase  in  the  number  of  ions,  it  must  be  due 
to  an  increase  in  their  speed.  This  increased  velocity  is  doubt- 
less connected  with  the  diminution  in  the  internal  friction  of 
the  medium  with  rise  of  temperature,  and  the  consequent 
diminished  resistance  to  the  passage  of  the  ions  (p.  253). 

Grotthus'  Hypothesis  of  Electrolytic  Conductivity- 
Long  before  the  establishment  of  the  electrolytic  dissociation 
theory,  Grotthus  put  forward  a  hypothesis  to  account  for  the 
conductivity  of  electrolytes  which  is  of  considerable  historical 
interest.  He  assumed  that  under  the  influence  of  the  charged 
electrodes  the  molecules  of  the  salt,  e.g.,  potassium  chloride, 
arrange  themselves  in  lines  between  the  electrodes  so  that  the 
potassium  atoms  are  all  turned  to  the  negative  electrode,  and 
the  chlorine  atoms  to  the  positive  electrode.  Electrolysis 
takes  place  in  such  a  way  that  the  external  potassium  atom  is 
liberated  at  the  cathode  and  the  chlorine  atom  at  the  anode. 
The  potassium  atom  which  is  left  free  at  the  anode  unites  with 
the  chlorine  atom  of  the  molecule  next  to  it,  the  chlorine  atom 
of  the  latter  with  a  potassium  atom  of  the  molecule  next  in  the 
chain,  and  so  on.  A  similar  process  takes  place  starting  at  the 
anode,  in  other  words,  an  exchange  of  partners  takes  place 
right  along  the  chain,  from  one  electrode  to  the  other.  Under 
the  influence  of  the  charged  electrodes,  the  new  molecules  twist 
round  till  they  are  in  the  former  relative  position,  when  the 
end  atoms  are  again  discharged,  and  so  electrolysis  proceeds. 

The  fatal  objection  to  this  ingenious  theory  is  that  a  con- 
siderable E.M.F.  would  have  to  be  employed  before  any 
decomposition  whatever  takes  place,  hence  Ohm's  law  would 
not  hold  (cf.  p.  241). 

Practical  Illustrations — The  following  experiments,  which 


ELECTRICAL  CONDUCTIVITY  265 

are  fully  described  in  the  course  of  the  chapter,  may  readily  be 
performed  by  the  student : — 

(1)  Experiment  on  the  migration  velocity  of  the  ions  (p.  246). 

(2)  Rough   determination  of  the  absolute   velocity  of  the 
MnO4'  ion  (p.  254). 

(3)  Determination  of  the  constant  of  conductivity  vessel  with 
«/5o  potassium  chloride.     (The  specific  conductivity,  K,  of  this 
solution  at  different  temperatures  is  as  follows  :  0-001522  at  o°, 
0-001996  at  10°,  0*002399  at  18°,  and  0-002768  at  25°.) 

(4)  Determination  of  the  specific  and  molecular  conductivities 
of  solutions  of  sodium  chloride  and  of  succinic  acid. 

As  the  conductivity  of  solutions  varies  greatly  with  the  tem- 
perature, the  conductivity  vessel  must  be  partially  immersed  in 
a  thermostat  while  measurements  are  being  made. 

In  the  case  of  sodium  chloride,  measurements  may  be  made 
with  n/i,  n/io  and  n/ioo  solutions,  and  the  values  obtained 
for  the  molecular  conductivity  compared  with  those  given  in 
Kohlrausch's  tables.1  The  results  in  very  dilute  solutions  are 
not  trustworthy  unless  great  attention  is  paid  to  the  purification 
of  the  water  used  in  making  up  the  solutions. 

In  the  case  of  succinic  acid,  it  is  usual  to  start  with  a  1/16 
wolar  solution;  20  c.c.  of  this  solution  is  placed  in  the  con- 
ductivity cell  in  the  thermostat,  and  when  the  temperature  is 
constant  the  resistance  is  determined.  10  c.c.  of  the  solution 
is  then  removed  with  a  pipette,  10  c.c.  of  water  at  the  same 
temperature  added,  the  resistance  again  determined  after 
thoroughly  mixing  the  solution,  and  so  on.  Measurements  are 
thus  made  in  dilutions  of  16,  32,  64,  128,  256,  512  and  1024 
litres.  From  the  values  of  /*„  thus  obtained,  the  degree  of 
dissociation  can  be  calculated  by  the  usual  formula  a  =  ^J^^  . 
/AOO  in  this  case  can  only  be  determined  indirectly ;  its  value  at 
25°  is  about  381.  From  the  values  of  a  in  different  dilutions, 
K,  the  dissociation  constant  of  the  acid  may  then  be  calculated  ; 
according  to  Ostwald,  K  =  0*000066  at  25°. 

1  Full  details  of  electrical  conductivity  measurements  and  a  large  amount 
of  conductivity  data  are  given  in  Kohlrausch  and  Holborn,  Leitvermogen 
der  Elektrolytc,  Leipzig,  1898. 


CHAPTER  XI 

EQUILIBRIUM  IN  ELECTROLYTES.     STRENGTH  OF 
ACIDS  AND  BASES.     HYDROLYSIS 

The  Dilution  Law  —  In  a  previous  chapter  it  has  been 
shown  that  chemical  equilibria,  both  in  gaseous  and  liquid 
systems,  can  be  represented  satisfactorily  by  means  of  the  law 
of  mass  action.  We  have  now  to  apply  this  law  to  binary 
electrolytes,  on  the  assumption  that  the  ions  are  to  be  re- 
garded as  independent  entities. 

According  to  the  electrolytic  dissociation  theory,  an  aqueous 
solution  ol  acetic  acid  contains  molecules  of  non-ionised  acid 
in  equilibrium  with  its  ions,  represented  by  the  equation 

CH3COO'  +  H-^CH8COOH. 

Suppose  in  the  volume  v  of  solution  the  total  concentration  of 
the  acid  is  i,  and  that  a  fraction  of  it,  represented  by  a,  is 
split  up  into  ions.  The  concentration  of  the  undissociated 

acid  is  -     —  ,  that  of  each  of  the  ions  (since  they  are  neces- 

sarily present  in  equivalent  amount)  -.      Hence,  from  the  law 

of  mass  action, 

©2  /i  -  a\  a2 

=  K(  -     -  )  or  7  -  r-  =  K  .         .       (i) 
\     V      )         (i   -  a)v 

where  K,  as  before,  is  the  equilibrium  constant.  For  conduc- 
tivity measurements,  the  above  formula  may  be  put  in  a  rather 
different  form  by  substituting  PV/PQQ  for  a.  It  then  becomes 


266 


EQUILIBRIUM  IN  ELECTROLYTES  267 


--K. 


It  is  preferable,  however,  to  remember  the  dilution  formula  in 
the  first  form. 

This  relationship,  which  is  known  as  Ostwald's  dilution  law, 
may  be  tested  by  substituting  a  value  for  a  (from  conductivity 
or  osmotic  observations)  at  any  dilution  v,  and  calculating  K, 
the  equilibrium  constant  ;  the  value  of  a  at  any  other  dilution 
may  then  be  obtained  from  the  formula  and  compared  with 
that  determined  directly.  This  was  done  (from  conductivity 
measurements)  by  van't  Hoff  and  Reicher,  and  the  results  are 
given  in  the  accompanying  table  :  — 

Acetic  acid:  K  =  0-0000178  at  14*1°;  /x^,  =  316. 

v  (in  litres)  .         .  0*994  2'02  I5'9  I^*i  1500  3010  7480  15000 

/*,  1-27  1-94       5*26  5*63  46'6  64-8  95-1  129 

1000  (observed)    .  0*40  0-614     *'66  1*78  14-7  20-5  30-1  40-8 

1000  (calculated)  .  0-42  0-6         1-67  1-78  15*0  20*2  30-5  40-1 

The  agreement  between  observed  and  calculated  values  is 
excellent  ;  it  is,  in  fact,  much  closer  than  for  any  case  of 
ordinary  dissociation  so  far  investigated.  The  table  also 
shows  how  small  is  the  dissociation  of  acetic  acid  solutions 
under  ordinary  conditions  ;  a  molar  solution  is  ionised  only  to 
the  extent  of  0*4  per  cent.,  and  even  a  1/1500  molar  solution 
rather  less  than  1  5  per  cent. 

The  dilution  law  holds  for  nearly  all  organic  acids  and  bases, 
but  does  not  hold  for  salts,  or  for  certain  mineral  acids  and 
bases.  The  latter  point  is  discussed  in  a  later  section. 

When  the  deg  ree  of  dissociation  is  small,  as  in  the  case  of 
acetic  acid  for  fairly  concentrated  solution,  a  can  be  neglected 
in  comparison  with  i,  and  the  dilution  law  then  becomes 

o 

—  =  K  or  a  =    N/Kz;    .  (2) 

v  ^  ' 

that  is,  for  weak  electrolytes  the  degree  of  dissociation  is  approxi- 
mately proportional  to  the  square  root  of  the  dilution.  When 


268       OUTLINES  OF  PHYSICAL  CHEMISTRY 

a  cannot  be  neglected  in  comparison  with   i,  a  is  given  by  the 
equation 


Kv         l 
=  ~  T~  +  V 


obtained  by  solving  equation  (i)  for  a.  In  order  to  familiarise 
himself  with  the  use  of  the  dilution  formula,  the  student  should 
calculate  a  for  acetic  acid  in  different  dilutions  from  the  value 
of  K  given  above  both  by  the  approximate  and  accurate 
formula. 

The  physical  meaning  of  the  constant  K  will  be  clear  if 
a  in  the  dilution  formula  (i)  is  put  =  •£.  Then  2K  =  i/v, 
that  is,  2K  is  the  reciprocal  of  the  volume  at  which  the 
electrolyte  is  dissociated  to  the  extent  of  50  per  cent.  Acetic 
acid,  for  instance,  will  be  half  dissociated  at  a  dilution  of 

:  -  0*  =  2  7)7  7  7  n'tres  (ff-  table). 

2  X  O'OOOOlS 

As  the  method  of  deriving  it  indicates,  the  dilution  law 
applies  only  to  binary  electrolytes,  i.e.,  electrolytes  which  split 
up  into  two  ions  only,  and  it  is  not  therefore  a  priori  probable 
that  it  will  hold  for  dibasic  acids,  such  as  succinic  acid,  which 
presumably  dissociate  according  to  the  equation 

C2H4(COOH)22C2H4(COO)2"  +  2H-. 

It  is,  however,  an  experimental  fact  that  when  the  concentration 
of  succinic  acid  is  expressed  in  mols  (not  in  equivalents)  per 
litre,  the  values  of  K  obtained  by  substitution  in  the  dilution 
formula  remain  constant  through  a  wide  range  of  dilution. 
This  indicates  that  the  acid  at  first  splits  up  into  two  ions  only, 
doubtless  according  to  the  equation 

„  /COOH_>r      /COO'         „. 
4<-^2    4\COOH  1 


and  that  the  second  possible  stage,  represented  by  the  equation 


/COO'    _>rFr/COO"     H 
<-^2    4\COO  1 


EQUILIBRIUM  IN  ELECTROLYTES  269 

is  not  appreciable  under  the  conditions  of  the  experiment.  In 
other  cases,  however,  e.g.,  fumaric  acid,  the  value  of  K  increases 
with  dilution  before  the  dilution  has  progressed  very  far,  which 
indicates  that  the  second  stage  of  the  dissociation  early  becomes 
of  importance. 

Strength  of  Acids — We  are  accustomed  to  estimate  the 
strength  of  acids  in  a  roughly  qualitative  way  by  their  relative 
displacing  power.  Sulphuric  acid,  for  example,  is  usually  re- 
garded as  a  strong  acid,  because  it  can  displace  such  acids  as 
acetic  and  hydrocyanic  from  combination.  This  principle  can 
be  developed  to  a  quantitative  method  for  estimating  the  rela- 
tive strengths  of  acids  (and  bases)  if  care  is  taken  to  make  the 
comparison  under  proper  conditions.  This  is  sufficiently  secured 
by  making  the  experiments  in  a  homogeneous  system  under  such 
conditions  that  all  the  reacting  substances  and  products  of  reaction 
remain  in  the  system.  We  learn  in  studying  inorganic  chemistry 
that  many  reactions  proceed  wholly  or  partially  in  a  particular 
direction  for  two  main  reasons :  (a)  because  an  insoluble  (or 
practically  insoluble)  product  is  formed  which  is  thus  removed 
from  the  reacting  system, 

e.g.,  Na2SO4  +  BaCl2  -»  2NaCl  +  BaSO4  (insoluble) ; 
(b)  because  a  volatile  product  is  formed  which  under  the  con- 
ditions of  experiment  leaves  the  reacting  system, 

e.g.,  2NaCl  +  H2SO4->Na2SO4  +2HC1  (volatile). 

Such  reactions  are  obviously  unsuitable  for  determining  the 
relative  strengths  of  the  acids  concerned. 

Bearing  these  considerations  in  mind,  we  now  proceed  to 
investigate  the  relative  strengths  of,  say,  nitric  and  dichloracetic 
acids  by  bringing  them  in  contact  with  an  amount  of  base  insuffi- 
cient to  saturate  both  of  them,  and  find  how  the  base  distri- 
butes itself  between  the  two  acids.  If,  for  example,  the  acids 
are  taken  in  equivalent  amount,  and  sufficient  base  is  taken  to 
saturate  one  of  them,  we  have  to  determine  the  position  of 
equilibrium  represented  by  the  equation 


270         OUTLINES  OF  PHYSICAL  CHEMISTRY 

CHClgCOOK  +  HNO32CHC12COOH  +  KNO3. 
It  is  evident  that  no  chemical  method  would  answer  the  purpose, 
because  it  would  disturb  the  equilibrium.  When,  however,  a 
physical  property  of  one  of  the  components,  which  alters  with 
the  concentration,  can  be  measured,  the  position  of  equilibrium 
can  be  determined.  A  method  used  for  this  purpose  by  Ostwald, 
depending  on  the  changes  of  volume  on  neutralization,  will  be 
readily  understood  from  an  example. 

When  a  mol  of  potassium  hydroxide  is  neutralized  by  nitric 
acid  in  dilute  solution,  there  is  an  increase  of  volume  of  about 
20  c.c.  When,  on  the  other  hand,  the  same  quantity  of  alkali 
is  neutralized  by  dichloracetic  acid,  the  increase  of  volume  is 
about  13  c.c.  It  is  therefore  clear  that  the  complete  displace- 
ment of  dichloracetic  acid  by  nitric  acid,  according  to  the 
equation 

CHC12COOK  +  HN03  ->  CHC12COOH  +  KNO3, 
would  give  an  increase  of  volume  of  (20  -  13)  =  7  c.c. ;  if  no 
displacement  took  place,  there  would,  of  course,  be  no  change 
of  volume.     The  change  actually  observed  was  5-67  c.c.,  which 
means  that  the  reaction  represented  by  the  equation  has  gone 

from  left  to  right  to  the  extent  of  -~ —  =  80  per  cent,  approxi- 
mately ;  in  other  words,  the  nitric  acid  has  taken  80  per  cent,  of 
the  base,  and  20  per  cent,  has  remained  combined  with  the 
dichloracetic  acid.  The  relative  strength,  or  relative  activity, 
of  the  acids  under  these  conditions  is  therefore  80  :  20  or  4  :  i. 

Any  other  physical  property,  which  is  capable  of  quantitative 
measurement  and  differs  from  the  two  systems,  can  be  equally 
well  employed  for  the  determination  of  equilibrium.  The  heat 
of  neutralization  has  been  used  for  this  purpose  by  Thomsen, 
and  the  measurement  of  the  refractive  index  by  Ostwald ;  the 
principle  of  the  methods  is  exactly  the  same  as  in  the  example 
just  given. 

Thomsen's  therm ochemical  measurements  were  the  first  to 


EQUILIBRIUM  IN  ELECTROLYTES  271 

be  made  on  this  subject,  and  he  arranged  the  different  acids 
in  the  order  of  their  "  avidities  "  or  activities.  Ostwald  then 
showed  that  the  same  order  of  the  avidities  was  obtained  by 
the  volume  and  refractivity  methods,  and,  further,  that  the  results 
were  independent  of  the  nature  of  the  base  competed  for,  so 
that  the  avidities  are  specific  properties  of  the  acids. 

The  relative  strength  of  acids  can  also  be  determined  on  an 
entirely  different  principle,  depending  on  kinetic  measurements. 
It  has  already  been  pointed  out  that  acids  accelerate,  in  a 
catalytic  manner,  the  hydrolysis  of  cane  sugar,  of  methyl  acetate, 
acetamide,  etc.  Ostwald  made  many  experiments  on  this  sub- 
ject and  reached  the  very  important  conclusion  that  the  order 
of  the  activity  of  acids  is  the  same,  whether  measured  by  the 
distribution  method  (which  is,  of  course,  a  static  method),  or 
by  a  kinetic  method.  This  affords  further  evidence  in  favour 
of  the  conclusion  just  mentioned,  that  the  activity  or  affinity  is 
a  specific  property  of  the  particular  acid,  independent  of  the  method 
by  which  it  is  measured. 

Thus  far  had  our  knowledge  of  the  subject  progressed  when 
in  1884  the  first  paper  of  Arrhenius  appeared.  He  showed 
that  the  order  of  the  "strengths"  of  the  acids  as  determined 
by  the  methods  just  described  is  also  that  of  their  electrical 
conductivities  in  equivalent  solution.  This  fundamentally  im- 
portant fact  is  illustrated  in  the  accompanying  table,  in  which 
the  conductivities  of  the  acids  in  normal  solution  are  quoted, 
that  of  hydrochloric  acid  being  taken  as  unity. 

Relative  Activity. 

Acid.           Thermochemical.  Cane  Sugar.       Conductivity. 

Hydrochloric             100  100  100 

Nitric                         100  100  99-6 

Sulphuric                    49  53-6  65-1 

Monochloracetic           9  4' 8  4-9 

Acetic  0-4  1-4 

We  have  seen  that,  according  to  the  electric  dissociation 
theory,  the  electrical  conductivity  of  an  acid  is  mainly  deter- 


272       OUTLINES  OF  PHYSICAL  CHEMISTRY 

mined  by  its  degree  of  dissociation;  for  example,  the  con- 
ductivity of  a  normal  solution  of  acetic  acid  is  small  because 
it  is  ionised  only  to  a  very  small  extent.  Further,  owing  to  the 
predominant  share  taken  by  the  hydrogen  ions  in  conveying 
the  current  (p.  252),  the  relative  conductivities  of  acids  will  be 
approximately  proportional  to  their  H*  ion  concentrations.  It 
is  therefore  natural  to  suppose  that  the  activity  of  acids,  as 
illustrated  by  distribution  and  catalytic  effects,  is  also  due  to 
that  which  all  acids  have  in  common,  namely,  hydrogen  ions. 
This  assumption  is  in  complete  accord  with  the  experimental 
results,  as  the  following  illustration  shows.  The  velocity  con- 
stant for  the  hydrolysis  of  cane  sugar  in  the  presence  of  1/80 
normal  hydrochloric  acid  is  0*00469  at  54*3°  (time  in  minutes) ; 
as  the  acid  may  be  regarded  as  completely  dissociated  CH-  = 
0-0125.  CH-  for  1/4  normal  acetic  acid  (^  =  4,  cf.  p.  267)  may 
be  calculated  from  the  dilution  formula  or  directly  from  the 
equilibrium  equation  as  follows  : — 

[H-][CH3COO']  _         [H-P  [H-p 

[CH3COOH]        [CH3COOH]      [0-25  -  H-]~ 

whence  CH-  =  0-002. 

On  the  assumption  that  the  catalytic  effect  of  acids  is  propor- 
tional to  the  H4  ion  concentration,  the  value  of  the  velocity 
constant,  x,  for  the  hydrolysis  of  cane  sugar  by  0*25  normal 
acetic  acid  at  5  4'  3°  should  be 

o'oi25  :  0*00469  :  :  0-002  :  x, 

whence  x  =  0-00075.  This  is  identical  with  the  result  obtained 
experimentally  by  Arrhenius,  and  we  have  here  a  very  striking 
confirmation  of  the  electrolytic  dissociation  theory. 

From  the  above  considerations,  we  conclude  that  the  charac- 
teristic properties  which  acids  have  in  common,  such  as  sour 
taste,  action  on  litmus,  catalytic  activity,  property  of  neutralizing 
bases,  etc.,  are  due  to  the  presence  of  H-  ions.  It  must  be 
remembered  that  direct  proportionality  between  H-  ion  concen- 
tration and  conductivity  is  neither  observed  nor  to  be  expected 


EQUILIBRIUM  IN  ELECTROLYTES 


273 


from  the  theory  ;  the  approximate  proportionality  is  due  to  the 
great  velocity  of  the  hydrogen  ions,  and  would  be  altogether 
absent  if  the  anions  were  the  more  rapid. 

As  there  is  a  simple  relationship  between  the  H-  ion  con- 
centration of  weak  acids  and  their  dissociation  constants  (p.  267), 
it  is  clear  that  the  behaviour  of  an  acid  can  be  to  a  great  extent 
foretold  when  its  dissociation  constant  has  been  measured.  Such 
determinations  have  been  made  for  a  great  number  of  weak 
acids  by  Ostwald  and  others,  and  some  of  the  results  are  given 
in  the  accompanying  table,  which  shows  very  clearly  how  greatly 
the  value  of  K  differs  for  different  acids,  and  the  influence  of 
substitution  :  — 


Acid. 

Acetic  H  •  CH3COO 
Monochloracetic  H  •  CH2C1COO 
Trichloracetic  H  •  C13COO 
Cyanacetic  H  •  CH2CNCOO 
Formic  H  •  HCOO 
Carbonic  H  •  HCO3 
Hydrogen  sulphide  H  •  SH 
Hydrocyanic  H  •  CN 
Phenol  H  •  OC6H6 


Value  of  K  at  25°  (v  in  litres). 
0-000018  =  180,000  x  io-10 
0-00155 


0-0037 

0-000214 


3040  x  io-10 

570  x  io-10 

13  x  io~10 

1*3  x  io-16 


For  a  weak  acid,  a=  vKz;,  where  a  is  the  degree  of  dis- 
sociation at  the  volume  v.  Hence,  for  two  acids  at  the  same 
dilution  a/a'  =  \/K/K',  or  the  ratio  of  the  degrees  of  dissocia- 
tion is  equal  to  the  square  root  of  the  ratio  of  the  dissociation 
constants.  From  the  data  given  in  the  table  it  can  readily  be 
calculated  that  in  solutions  of  monoch  loracetic  and  acetic  acid 
of  the  same  concentration  the  ratio  of  the  H*  ion  concentrations 
is  approximately  9*3  :  i.  The  effect  of  replacing  one  of  the 
hydrogens  in  acetic  acid  by  chlorine  is  thus  to  form  a  much 
stronger  acid  and  the  CN  group  has  a  still  greater  effect,  as  the 
table  shows. 

A  further  important  point  is  the  effect  of  dilution  on  the 
"strength"  of  an  acid.  As  the  degree  of  dissociation  in- 
creases regularly  with  dilution,  it  is  evident  that  the  activity  of 
a  weak  acid  will  approach  nearer  and  nearer  to  that  of  a  strong 
18 


274       OUTLINES  OF  PHYSICAL  CHEMISTRY 

acid  (which  is  completely  active  in  moderate  dilution)  until 
finally,  when  the  weak  acid  is  completely  ionised,  it  will  have 
the  same  strength  as  the  strong  acid  in  equivalent  dilution.  It 
follows  that  the  strength  of  acids  is  the  more  nearly  equal  the 
more  dilute  the  solution,  and  that  at  "  infinite  dilution  "  all 
acids  are  equally  strong.  It  can  readily  be  calculated  from  the 
conductivity  tables  that  the  relative  strengths  of  hydrochloric 
and  acetic  acids  in  different  dilutions  are  as  follows  : — 

Concentration                w/i  w/io  w/ioo  M/IOOO  n/io,ooo 

a  for  HC1                     0*81  0-91  0*97  0-99             i'o 

a  for  HC2H3O2           o'oo4  0-013  0^04  0-13             0-4 

Ratio  HC1/HC2H3O2   200         70  24  7-5             2-5 

Strength  of  Bases — Just  as  the  strength  of  acids  depends 
on  their  concentration  in  hydrogen  ions,  so  the  strength  of 
bases  depends  on  the  concentration  in  hydroxyl  ions.  On  this 
view,  potassium  hydroxide  is  a  strong  base,  because  in  moderate 
dilution  it  is  almost  completely  ionised  according  to  the  equa- 
tion KOH  t^  K*  +  OH' ;  ammonium  hydroxide,  on  the  other 
hand,  is  a  weak  base,  because  its  aqueous  solution  contains  only 
a  relatively  small  concentration  of  OH'  ions.  Since  certain 
organic  compounds,  including  amines  and  alkaloids,  have  basic 
properties,  their  aqueous  solutions  must  also  contain  OH'  ions. 
Thus,  solutions  of  pyridine,  C5H5N,  contain  not  only  the  free 
base,  but  a  certain  concentration  of  C5H6N'  and  OH'  ions,  in 
equilibrium  with  the  undissociated  hydrate,  as  represented  by 
the  equation 

C5H6NOH^C6H6N-  +  OH'. 

The  strength  of  bases  may  be  determined  by  distribution  or 
catalytic  methods,  corresponding  with  those  already  described 
for  determining  the  strength  of  acids,  as  well  as  by  conductivity 
methods.  A  fairly  satisfactory  catalytic  method  is  the  effect 
on  the  rate  of  condensation  of  acetone  to  diacetonyl  alcohol,1 
represented  by  the  equation 

2CH3COCH3  -»  CH3COCH2C(CH3)2OH. 

^oelichen,  Zeitsch.  PhysikalChem.,  1900,  33,  129. 


EQUILIBRIUM  IN  ELECTROLYTES  275 

The  order  of  the  strength  of  bases  as  determined  by  this  method 
agrees  with  the  results  of  conductivity  measurements.  Another 
method,  which  is  not  purely  catalytic,  since  the  base  is  used  up 
in  the  process,  is  the  effect  on  the  hydrolysis  or  saponification 
of  esters  (p.  207).  This  process  is  usually  represented  by  the 
typical  equation 

CH3COOC2H5  +  KOH  =  CH3COOK  +  C2H5OH. 
Experience  shows,  however,  that  for  the  so-called  strong  bases, 
which  are  almost  completely  ionized  in  moderate  dilution,  the 
rate  of  hydrolysis  is  practically  independent  of  the  nature  of 
the  cation  (whether  K,  Na,  Li,  etc.),  a  fact  which  is  readily 
accounted  for  on  the  view  that  the  ions  exist  free  in  solution, 
as  the  ionic  theory  postulates,  and  that  the  OH'  ions  are  alone 
active  in  saponification.  The  general  equation  for  the  hy- 
drolysis of  ethyl  acetate  by  bases  may,  therefore,  be  written  as 
follows — 

CH3COOC2H5  i-  OH'  =  CH3COO'  +  C2H5OH. 
The  relative  strength  of  bases,  as  obtained  from  their  efficiency 
in  saponifying  esters,  is  in  excellent  agreement  with  their 
strength  as  deduced  from  conductivity  measurements.  The 
ionization  view  of  the  saponification  of  esters  is  further  sup- 
ported by  the  fact  that  the  reaction  between  ethyl  acetate  and 
barium  hydroxide  is  bimolecular  and  not  trimolecular,  as  would 
be  anticipated  if  it  proceeded  according  to  the  equation 

2CH3COOC2H5  +  Ba(OH)2  =  (CH3COO)2Ba  +  2C2H5OH. 

The  alkali  and  alkaline  earth  hydroxides  are  very  strong 
bases,  being  ionized  to  about  the  same  extent  as  hydrochloric 
acid  in  equivalent  dilution.  Bases  differ  as  greatly  in  strength 
as  do  acids ;  the  dissociation  constants  for  a  few  of  the  more 
important  are  given  in  the  table. 


Base. 

Ammonia  NH4'OH 
Methylamine  CH3NH3'OH 
Trimethylamine  (CH3)3NH'OH 
Pyridine  C5H6N-OH 
Aniline  C6H6NH3'OH 


Value  of  K  (25°)  (v  in  litres] 
0-000023  =  230,000  x  io~10 
©•00050 
0-000074 

23  x  io-10 

4-6  x  io~10 


276       OUTLINES  OF  PHYSICAL  CHEMISTRY 

Interesting  results  have  been  obtained  as  to  the  effect  of  sub- 
stitution on  the  strength  of  bases.  Thus  the  table  shows  that 
the  basic  character  is  increased  by  replacing  one  of  the  hydrogen 
atoms  in  ammonia  by  the  CH3  group,  but  is  greatly  diminished 
by  the  C6H5  group. 

Mixture  of  two  Electrolytes  with  a  Common  Ion  —  The 
dissociation  of  weak  acids  and  bases  is  greatly  diminished  by 
the  addition  of  a  salt  with  an  ion  common  to  the  acid  or  base. 
For  example,  the  equilibrium  in  a  solution  of  acetic  acid  is  re- 
presented  by  the  equation  [H-]  [CH3COO'J  =  K  [CH3COOH], 
and  if  by  adding  sodium  acetate  the  CH3COO'  ion  con- 
centration is  greatly  increased,  the  H*  ion  concentration  must 
correspondingly  diminish,  since  the  concentration  of  the  undis- 
sociated  acid  cannot  be  greatly  altered  (nearly  the  whole  of  the 
acid  being  present  in  that  form  in  the  original  solution)  and 
therefore  the  right-hand  side  of  the  equation  is  practically 
constant. 

The  exact  equations  representing  the  mutual  influence  of 
electrolytes  with  a  common  ion  are  somewhat  complicated,  but 
an  approximate  formula  which  is  often  useful  can  be  obtained 
as  follows  :  If  the  total  concentration  of  a  binary  electrolyte  is 
c  and  its  degree  of  dissociation  is  a,  we  have,  from  the  law  of 
mass  action, 

M-K.         ...       (i) 

- 


If  now  an  electrolyte  with  a  common  ion  is  added,  and  the 
concentration  of  the  latter  is  c0,  the  above  equation  becomes 

(ac)(a'c  +  Co)   _  K  (. 

(l   -  a> 

This  equation  is  quite  accurate.  As  K,  c  and  c0  are  known,  a', 
where  a'  is  the  new  degree  of  dissociation,  can  be  calculated, 
perhaps  most  readily  by  successive  approximations. 

If  the  degree  of  dissociation  of  the  first  electrolyte  is  small, 
i  -  a'  can  be  taken  as  unity  without  appreciable  error  ;  further, 


EQUILIBRIUM  IN  ELECTROLYTES  277 

if  the  second  electrolyte  is  highly  ionised  and  is  added  in  con- 
siderable proportion,  aV  can  be  neglected  in  comparison  with 
cot  and  equation  (2)  simplifies  to 

(aV)  Co  =  K.      .         .         .         .       (3) 

Otherwise  expressed,  the  concentration  of  one  of  the  ions  of  a 
weak  electrolyte  is  inversely  proportional  to  the  ionic  concentra- 
tion of  a  highly-dissociated  salt  having  an  ion  in  common  with 
the  other  ion  of  the  weak  electrolyte. 

As  an  illustration  of  the  application  of  the  last  equation,  we 
will  consider  the  effect  of  the  addition  of  an  equivalent  amount 
of  sodium  acetate  on  the  strength  of  0*25  molar  acetic  acid.  In 
this  dilution  a  for  the  acid  is  0*0085  an(*  °*  =  0-0085  x  0-25  = 
o'oo2i  =  CR'.  In  0*25  molar  solution,  sodium  acetate  is 
dissociated  to  the  extent  of  69-2  per  cent.,  hence  c0  = 
0*25  x  0*692  =  0*173.  We  have,  therefore, 

a'  x  0*173  =  0*000018,  whence  a'  =  o'oooi. 

ac  is  therefore  0*25  x  0*0001  =0*000025=  CR.  in  presence  of 
0-25  molar  sodium  acetate,  so  that  the  strength  of  the  acid  is 
diminished  in  the  ratio  85  :  i.  In  an  exactly  similar  way,  the 
strength  of  ammonia  as  a  base  is  greatly  reduced  by  the  addi- 
tion of  ammonium  salts. 

This  action  of  neutral  salts  on  weak  bases  and  acids  is  largely 
taken  advantage  of  in  analytical  chemistry.  For  example,  the 
concentration  of  OH'  ions  in  ammonia  solution  is  sufficient  to 
precipitate  magnesium  hydroxide  from  solutions  of  magnesium 
salts,  but  in  the  presence  of  ammonium  chloride  the  OH'  ion 
concentration  is  so  greatly  reduced  that  precipitation  no  longer 
occurs.  Similarly,  the  addition  of  hydrochloric  acid  diminishes 
the  concentration  of  S"  ions  in  hydrogen  sulphide  to  such  an 
extent  that  zinc  salts  are  no  longer  precipitated  (cf.  p.  300). 

Isohydric  Solutions — It  is  of  particular  interest  to  inquire 
what  must  be  the  relation  between  two  solutions  with  a  common 
ion — two  acids,  for  example — in  order  that,  when  mixed,  they 
may  exert  no  mutual  influence.  This  problem  was  investigated 


278       OUTLINES  OF  PHYSICAL  CHEMISTRY 

both  theoretically  and  practically  by  Arrhenius,  who  showed  that 
no  alteration  in  the  degree  of  dissociation  of  either  of  the  salts 
(acids  or  bases)  takes  place  when  the  concentration  of  the  common 
ion  in  the  two  solutions  before  mixing  is  the  same.  Such  solu- 
tions are  termed  isohydric. 

The  relative  dilutions  in  which  two  acids  or  other  electrolytes 
with  a  common  ion  are  isohydric  can  readily  be  calculated  from 
their  dissociation  constants.  The  value  of  K  for  acetic  acid  is 
0-000018,  and  for  cyanacetic  acid  0*0037,  both  at  25°.  Since 
a  =  *jKv  approximately,  it  is  clear  that  the  degree  of  dissocia- 
tion, a,  will  be  the  same  for  the  two  acids  when  the  dilutions 
are  inversely  as  the  dissociation  constants.  The  dilution  of  the 
cyanacetic  acid  must  therefore  be  3700  :  18,  or  205  times  that 
of  acetic  acid  for  isohydric  solutions. 

Arrhenius  has  shown  that  by  the  principle  of  isohydric  solu- 
tions the  mutual  influence  of  electrolytes  with  a  common  ion 
even  of  strong  acids  and  their  neutral  salts,  can  be  calculated 
with  a  considerable  degree  of  accuracy,  but  the  methods  are 
somewhat  complicated  and  cannot  be  given  here.  Not  only  is 
the  degree  of  dissociation  of  a  weak  acid  greatly  influenced  by 
the  addition  of  a  strong  acid,  or  other  electrolyte  with  a  common 
ion,  but  the  latter  is  affected,  though  to  a  much  smaller  extent, 
by  the  presence  of  the  former.  It  can,  for  instance,  be  calcu- 
lated that  when  a  mol  of  acetic  acid  and  a  mol  of  cyanacetic 
acid  are  present  in  a  litre  of  water,  the  dissociation  of  the 
former  is  only  about  1/14  of  its  value  in  aqueous  solution, 
whilst  the  presence  of  the  acetic  acid  only  diminishes  the 
dissociation  of  the  cyanacetic  acid  by  0*25  per  cent. 

Mixture  of  Electrolytes  with  no  Common  Ion — The 
equilibrium  in  a  mixture  of  two  electrolytes  without  a  common 
ion  can  be  calculated  when  the  concentrations  and  dissociation 
constants  are  known,  but  the  calculation  is  somewhat  compli- 
cated. If  solutions  of  two  highly-dissociated  salts,  such  as 
potassium  chloride  and  sodium  bromide,  are  mixed,  small 
amounts  of  undissociated  sodium  chloride  and  potassium 


EQUILIBRIUM  IN  ELECTROLYTES  279 

bromide  will  be  formed  ;  but  as  the  salts  are  all  highly  dis- 
sociated, the  mutual  effect  is  very  small.  If  dissociation  is 
complete,  the  process  will  be  represented  by  the  equation 

K-  +  Cl' .+  Na-  +  Br'  =  K-  +  Cl'  +  Na-  +  Br', 
otherwise  expressed,  the  salts  will  exert  no  mutual  influence. 
These  considerations  account  for  the  observation  of  Hess 
(p.  148)  that  the  thermal  effect  of  mixing  dilute  solutions  of 
two  binary  salts  is  very  slight.  At  the  time  Hess  made  his 
observation,  it  was  extremely  puzzling,  because  it  was  known 
that  the  heats  of  formation  of  different  salts  were  very  different, 
and  therefore  heat  should  either  be  absorbed  or  given  out  as  an 
accompaniment  of  the  double  decomposition.  On  the  basis  of 
the  electrolytic  dissociation  theory,  however,  Hess's  results  at 
once  become  intelligible,  since  both  before  and  after  admixture 
the  solution  contains  mainly  the  same  free  ions. 

To  the  question  which  is  very  often  asked  as  to  what  com- 
pounds are  present  in  a  mixed  salt  solution,  it  must  therefore 
be  answered  that  all  the  undissociated  salts  and  ions  are  present 
which  can  be  formed  by  interaction  of  the  components,  and 
that  the  proportions  in  which  the  various  molecules  and  ions 
are  present  depend  on  the  concentrations  and  dissociation 
constants  of  the  various  salts. 

Dissociation  of  Strong  Electrolytes l — It  has  been  pointed 
out  (p.  267)  that  the  law  of  mass  action  holds  for  weak  (i.e., 
slightly  ionised)  electrolytes,  the  ions  being  regarded  as  inde- 
pendent units.  The  proof  of  the  applicability  of  the  law  has 
been  brought  more  particularly  by  Ostwald  from  the  results 
of  measurements  with  organic  acids.  It  is  a  remarkable  fact, 
however,  that  the  dilution  formula,  a2/(i  —  a)v  =  K,  which  is 
a  direct  consequence  of  the  law  of  mass  action,  does  not  appear 
to  be  valid  for  the  so-called  "  strong "  or  highly  dissociated 
electrolytes ;  when  the  values  of  a,  obtained  from  osmotic  or 
conductivity  measurements,  are  substituted  in  the  above  formula, 

lCf.  Drucker,  "Die  Anomalie  der  starken  Elektrolyte, "  Ahrens' 
Sammlung)  Stuttgart,  1905. 


28o        OUTLINES  OF  PHYSICAL  CHEMISTRY 

K  diminishes  greatly  with  dilution.  This  is  well  shown  in  the 
following  table  for  silver  nitrate.  The  first  column  contains 
v,  the  volume  in  litres  in  which  i  mol  of  the  salt  is  dissolved, 
in  the  second  column  is  given  the  value  of  a  calculated  from  con- 
ductivity measurements  at  25°,  and  in  the  third  column  are  given 
the  values  of  K  calculated  by  means  of  the  dilution  formula. 

16  0-8283  0-253  1<lr 

32  0-8748  0-191  1*16 

64  0-8993  0*127  I<06 

128  0-9262  0-122  1*07 

256  0*9467  0-124  1*08 

512  0*9619  0*125  1-09 

The  deviations  from   the  simple   law  appear   to    be   fairly 

regular  in  character,  and  van't  Hoff  has  proposed  an  empirical 

formula  which  represents  with  a   fair  degree  of  accuracy  the 

behaviour  of  the  great  majority  of  strong  electrolytes.     The 

formula  in  question  is  of  the  form 

which  may  also  be  written 

C3  /r*2       v 
d       u  ==         1 

where  Cd  represents  the  concentration  of  the  dissociated  part 
(the  ions),  CM  that  of  the  undissociated  part.  The  application 
of  this  formula  to  solutions  of  silver  nitrate  is  illustrated  in 
the  table,  and  it  will  be  observed  that  the  values  of  K1  in 
the  fourth  column  are  fairly  constant.  The  slightly  different 
formula  suggested  by  Rudolphi 


is  scarcely  as  satisfactory  as  that  of  van't  Hoff.  Some  observers 
have  suggested  a  generalised  form  of  van't  HofFs  formula,1  as 
follows : — 

Crf/C«  =  K3 
^/Bancroft,  Zeitsch.  Physikal  Client.,  1899,  31,  188. 


EQUILIBRIUM  IN  ELECTROLYTES  281 

and  experiment  shows  that  in  many  cases  n  does  not  differ 
much  from  1-5.  When  n  is  1-5  the  general  formula  reduces  to 
that  of  van't  Hoff. 

The  reason  why  the  law  of  mass  action  does  not  apply  to 
strong  electrolytes,  although  it  holds  so  accurately  for  weak 
electrolytes,  has  not  been  satisfactorily  elucidated.  It  was  long 
thought  that  the  values  of  a  obtained  from  the  results  of  con- 
ductivity measurements  were  not  the  true  values  of  the  degree 
of  dissociation,  but  recent  very  careful  comparison  shows  that 
the  results  obtained  by  conductivity  and  freezing-point  deter- 
minations in  dilute  solution  for  the  best-investigated  substances 
do  not,  as  a  rule,  differ  by  more  than  2  per  cent,  on  the 
average,  and  even  these  differences  may  be  due  largely  to 
experimental  error.1  In  a  few  cases  only  does  there  appear  to 
be  a  real  difference  between  the  results  obtained  by  the  two 
methods.  As  neither  of  the  values  for  a  gives  a  constant  value 
for  K  when  substituted  in  the  ordinary  dilution  formula,  there 
can  be  no  doubt  that  strong  electrolytes  do  behave  in  an 
anomalous  way. 

Several  disturbing  causes  might  be  suggested  to  account  for 
this  behaviour,  including  (a)  the  formation  of  complex  ions  by 
combination  of  the  ions  with  non-ionised  molecules;  (ft) 
mutual  influence  of  the  ions ;  (c)  interaction  of  the  ions  and 
the  solvent,  including  more  particularly  hydration  of  the  ions, 
and  one  or  more  of  these  effects  may  be  operative  in  any 
one  solution.  The  existence  of  complex  ions  in  solutions  has 
been  definitely  proved  by  Hittorf  and  others.  In  solutions  of 
cadmium  iodide,  for  instance,  there  is  evidence  that  I'  ions  unite 
with  CdI2  molecules  to  form  complex  ions  of  the  formula  CdI4". 
The  formation  of  complex  ions  would  diminish  the  number  of 
non-ionised  molecules  but  not  the  total  number  of  ions ;  it  would 
thus  affect  the  osmotic  pressure,  but  not  to  any  extent  the  con- 
ductivity. This  disturbing  effect  will  be  greatest  in  fairly  concen- 
trated solutions.  In  dilute  solutions  of  salts  of  the  alkalis  and 
1  Drucker,  loc.  cit. ;  Noyes,  Technology  Quarterly,  1904,  17,  293. 


282        OUTLINES  OF  PHYSICAL  CHEMISTRY 

alkaline  earths,  the  values  of  a  obtained  by  conductivity  and  os- 
motic pressure  methods  are  very  nearly  equal,  and  this  result 
appears  to  show  that  there  is  little  or  no  complex  ion  formation 
in  these  solutions. 

As  to  the  possible  effect  of  the  ions  on  each  other,  practically 
nothing  can  be  said  with  certainty.  The  fact  that  weak  electro- 
lytes follow  the  law  of  mass  action  through  a  very  wide  range 
of  dilution  may  be  connected  with  the  fact  that  under  all 
circumstances  the  ionic  concentration  is  small,  a  condition 
which  no  longer  holds  in  solutions  of  strong  electrolytes.  As 
to  how  and  to  what  extent  the  mutual  influence  is  exerted, 
little  or  nothing  is  known. 

The  possibility  of  the  interaction  of  the  ions  with  the  solvent 
has  been  much  discussed,  but  as  no  general  agreement  has  been 
reached  on  the  matter,  a  short  reference  to  the  subject  here  will 
suffice.  One  way  in  which  this  effect  might  influence  the  results 
would  be  if  the  ions  became  associated  with  a  large  proportion 
of  water  which  no  longer  acted  as  solvent.  The  effective  con- 
centrations of  an  ion  would  then  be  the  ratio  of  the  amount 
present  to  that  of  the  "  free  "  solvent,  instead  of  to  the  total 
solvent,  as  usually  calculated.  As,  however,  no  satisfactory 
method  of  estimating  the  relative  proportions  of  free  and  com- 
bined solvent  in  the  solution  of  an  electrolyte  has  yet  been 
suggested  the  question  is  at  present  mainly  of  theoretical  interest 

(P-  325) 

The  most  logical  method  so  far  suggested  for  dealing  with  the 

pro  blem  of  strong  electrolytes  is  due  to  Nernst.  He  considers 
that,  owing  to  their  mutual  influence,  the  activity  of  the  various 
substances  (ions  and  non-ionised  substances)  present  is  not  pro- 
portional to  their  respective  concentrations,  but  certain  correct- 
ing factors  have  to  be  applied  depending  on  the  extent  of  the 
mutual  influence.  Among  these  effects,  that  of  the  ions  on  each 
other  and  on  the  non-ionised  part  of  the  molecules,  as  well  as  the 
mutual  influence  between  ions  and  solvent,  seem  to  be  of  special 
importance,  but  so  far  comparatively  little  progress  has  been 


EQUILIBRIUM  IN  ELECTROLYTES  283 

made  with  the  determination  of  the  relative  magnitudes  of  the 
correcting  factors. 

Electrolytic  Dissociation  of  Water,  Heat  of  Neutral- 
ization —  So  far  we  have  regarded  the  usual  solvent  water 
simply  as  a  medium  for  dissociation,  but  there  is  evidence  to 
show  that  it  is  itself  split  up  to  a  very  small  extent  into  ions, 
according  to  the  equation 


Applying  to  this  equation  the  law  of  mass  action,  we  have,  as 
usual, 

[H-][OH']  =  K[H20], 

where  K  is  the  dissociation  constant  for  water.  As  the  ionic 
concentrations  are  extremely  small  the  concentration  of  the 
water  is.  practically  constant,  and  therefore  the  product  of  the 
concentration  of  the  ions 

[H-]  [OH']  =  Ko,,  a  constant. 

It  has  been  found  by  different  methods,  which  will  be  re- 
ferred to  later  (p.  293),  that  the  value  of  the  above  constant  at  25° 
is  about  1*2  x  10  *14.  In  pure  water  the  concentrations  of  the 
ions  are  necessarily  equal,  hence  CH  =  £OH'=  \/i'2  x  io~14  = 
i  -i  x  10  -  7  at  25°.  Otherwise  expressed,  this  means  that  pure 
water  contains  rather  more  than  i  mol  of  H>  and  OH'  ions,  that 
is,  i  gram  of  H1  ions  and  17  grams  of  OH'  ions,  in  io7  or 
10,000,000  litres.  The  ionic  product  is  independent  of  whether 
the  solution  is  acid  or  alkaline,  and  therefore  in  a  normal  solu- 
tion of  a  (completely  dissociated)  acid,  since  CH-  =  i,  COH'  is 
only  io  ~14,  and  in  a  solution  of  a  normal  alkali  Cu-  is  corre- 
spondingly small. 

These  considerations  are  of  great  importance  in  connection 
with  the  process  of  neutralization.  Assuming  that  the  solutes 
are  completely  ionised,  the  neutralization  of  i  mol  of  sodium 
hydroxide  by  hydrochloric  acid  in  dilute  solution  may  be  repre- 
sented as  follows  :  — 

Na  +  OH'  +  H-  +  Cl'  =  Na-  +  Cl'  +  H9O. 


284        OUTLINES  OF  PHYSICAL  CHEMISTRY 

Since  Na*  and  Cl'  ions  occur  in  equivalent  amount  on  each 
side,  they  may  be  neglected,  and  the  equation  reduces  to 


or,  otherwise  expressed,  the  combination  of  hydrogen  and 
hydroxyl  ions  to  form  water.  The  same  equation  applies  to 
the  neutralization  of  any  other  strong  base  by  a  strong  acid  ; 
provided  that  the  solutions  are  so  dilute  that  dissociation  is  prac- 
tically complete,  the  process  in  all  cases  consists  in  the  combination 
of  H'  and  OH'  ions  to  non-ionised  water.  It  may,  therefore,  be 
anticipated  that  for  equivalent  amounts  of  different  strong  bases 
and  acids  the  heat  of  neutralization  will  be  the  same,  and  that 
this  is  actually  the  case  is  shown  in  the  first  part  of  the  table. 
The  magnitudes  of  the  heats  of  neutralization  apply  for  molar 
quantities. 

Heats  of  Neutralization. 
Acid  and  Base.  Heat  of  Neutralization. 

HC1  and  NaOH  13,700  cal. 

HBr  and  NaOH  13,700  cal. 

HNO3  and  NaOH  13,700  cal. 

HC1  and  |Ba(OH)2  13,800  cal. 

NaOH  and  CH3COOH  13,400  cal. 

NaOH  and  HF  16,300  cal. 

HC1  and  ammonia  12,200  cal. 

HC1  and  dimethylamine  n,  800  cal. 

The  fact  that  the  heat  of  neutralization  of  strong  acids  and 
bases  is  independent  of  the  nature  of  the  acid  and  base  was 
long  a  puzzle  to  chemists,  and  the  simple  explanation  given 
above  is  one  of  the  conspicuous  triumphs  of  the  electrolytic 
dissociation  theory. 

Below  the  dotted  line  in  the  above  table  are  given  the  heats 
of  neutralization  of  two  weak  acids  by  a  strong  base  and  of  two 
weak  bases  by  a  strong  acid.  As  the  table  shows,  the  heat 
development  in  these  cases  may  be  more  or  less  than  13,700 
cal.  for  molar  quantities,  and  a  little  consideration  affords  a 
plausible  explanation.  The  neutralization  of  acetic  acid,  which 


EQUILIBRIUM  IN  ELECTROLYTES  285 

is  very  slightly  ionised,  by  sodium  hydroxide,  may  be  repre- 
sented by  the  equation 

CH3COOH  +  Na-  +  OH '  =  CH3COO  +  Na-  +  H2O, 
which  may  be  regarded  as  taking  place  in  two  stages — 
(i)  CH3COOH  =  CH3COO'  +  H-;  (2)  H-  +  OH'  =  H2O. 

The  heat  of  neutralization  is,  therefore,  the  sum  of  two  effects 
(i)  the  heat  of  dissociation  of  the  acid  ;  (2)  the  reaction 
H"  +  OH'  =  H2O,  which  gives  out  13,700  cal.  Hence,  since 
the  observed  thermal  effect  is  13,400  cal.  the  dissociation  of 
the  acid  must  absorb  300  calories.  For  hydrofluoric  acid,  on 
the  other  hand,  the  reaction  HF=  H-  +  F  is  attended  by  a  heat 
development  of  16,300  -  13,700  =  2,600  cal.  We  have  thus, 
an  approximate  method  of  determining  the  heat  of  ionisation 
of  electrolytes,  which  may  be  positive  or  negative. 

In  the  above  paragraphs  the  total  heat  change  has  been 
regarded  as  the  algebraic  sum  of  the  heats  of  neutralization 
and  of  ionisation,  but  it  is  probable  that  other  phenomena,  for 
example,  changes  of  hydration,  also  play  a  part. 

Hydrolysis — It  is  a  well-known  fact  that  salts  formed  by  a 
weak  acid  and  a  strong  base,  such  as  potassium  cyanide,  show  an 
alkaline  reaction  in  aqueous  solution,  whilst  salts  formed  by  the 
combination  of  a  weak  base  and  a  strong  acid,  for  example, 
ferric  chloride,  have  an  acid  reaction.  In  the  previous  section 
it  has  been  mentioned  that  water  is  slightly  ionised,  according 
to  the  equation  H2O  =  H-  -f  OH',  and  may  therefore  be  re- 
garded as  at  the  same  time  a  weak  acid  (since  H-  ions  are 
present)  and  a  weak  base  (owing  to  the  presence  of  OH'  ions). 
It  will  now  be  shown  that  the  behaviour  of  aqueous  solutions 
of  such  salts  as  potassium  cyanide  and  ferric  chloride  are  quanti- 
tatively accounted  for  on  the  assumption  that  water  is  electro- 
lytically  dissociated. 

In  a  previous  section  (p.  271)  it  has  been  pointed  out  that 
when  two  acids  are  allowed  to  compete  for  the  same  base,  the 
latter  distributes  itself  between  the  acids  in  proportion  to  their 


286         OUTLINES  OF  PHYSICAL  CHEMISTRY 

avidities,  and  it  has  also  been  shown  that  the  ratio  of  the 
avidities  of  two  acids  is  the  ratio  of  the  extent  to  which 
they  are  electrolytically  dissociated.  The  same  applies  to  a  salt 
in  aqueous  solution,  water,  in  virtue  of  its  hydrogen  ion  concen- 
tration^ being  regarded  as  one  of  the  competing  acids.  In  the 
case  of  a  salt  of  a  strong  acid,  such  as  sodium  chloride,  it 
would  not  be  anticipated  that  such  a  weak  acid  as  water  would 
take  an  appreciable  amount  of  the  base,  and  the  available 
experimental  evidence  quite  bears  out  this  expectation.  In 
other  words,  an  aqueous  solution  of  sodium  chloride  contains 
only  Na*  and  Cl'  ions  and  undissociated  sodium  chloride  in 
appreciable  amount,  and  is  therefore  neutral. 

The  case  is  quite  different  for  a  salt  formed  by  a  strong  base 
and  a  weak  acid,  such  as  potassium  cyanide.  Here  water  as 
an  acid  is  comparable  in  strength  to  hydrocyanic  acid,  and 
therefore  there  is  a  distribution  of  the  base  between  the  acid 
and  the  water  according  to  the  equation 

KCN  +  H2O^KOH  +  HCN, 

the  proportions  of  potassium  cyanide  and  potassium  hydroxide 
depending  upon  the  relative  strengths  of  water  and  hydrocyanic 
acid. 

From  the  equation  it  is  evident  that  potassium  hydroxide  and 
hydrocyanic  acid  must  be  present  in  equivalent  amount ;  and 
since  the  hydroxide  is  much  more  highly  ionised  than  hydro- 
cyanic acid,  the  solution  contains  an  excess  of  OH'  ions,  and 
must  therefore  be  alkaline,  as  is  actually  the  case. 

This  process  is  termed  hydrolysis,  i.e.,  decomposition  by 
means  of  water.  Similar  considerations  apply  to  the  salts 
formed  by  combination  of  weak  bases  and  strong  acids,  such 
as  aniline  hydrochloride.  As  water  is  comparable  in  strength 
to  aniline  as  a  base,  an  equilibrium  is  established  according  to 
the  equation 

C6H5NH3C1  +  HOH^C6H5NH3OH  +  HC1. 

In  this  case  there  is  an  excess  of  H-  ions,  as  hydrochloric  acid 


EQUILIBRIUM  IN  ELECTROLYTES  287 

is  much  more  highly  ionised  than  anilinium  hydroxide,  and 
therefore  the  solution  has  an  acid  reaction. 

A  salt  formed  by  the  combination  of  a  weak  acid  and  a 
weak  base,  e.g.,  aniline  acetate,  is  naturally  hydro lysed  to  a 
still  greater  extent.  These  three  types  of  hydrolytic  action 
will  now  be  considered  quantitatively. 

(a)  Hydrolysis  of  the  Salt  of  a  Strong  Base  and  a 
Weak  Acid — A  typical  salt  of  this  type  is  potassium  cyanide, 
the  hydrolytic  decomposition  of  which  is  represented  by  the 
equation 

KCN  +  HOH  ^  KOH  +  HCN, 

or,  according  to  the  electrolytic  dissociation  theory, 
K-  +  CN'  +  HOH^K-  +  OH'  +  HCN, 

on  the  assumption,  which  is  only  approximately  true,  that 
potassium  cyanide  is  completely  ionised  and  hydrocyanic  acid 
non-ionised. 

The  equilibrium  can  now  be  investigated,  and  the  extent  of 
the  hydrolysis  determined,  if  a  means  can  be  found  of  deter- 
mining the  equilibrium  concentration  of  one  of  the  reacting 
substances,  for  example,  the  OH'  ions.  This  could  not,  of 
course,  be  done  by  titrating  the  free  alkali,  as  the  equilibrium 
would  thus  be  disturbed,  but  one  of  the  methods  given  on 
p.27i  may  conveniently  be  used.  The  method  which  has  been 
most  largely  used  is  to  determine  the  effect  of  the  mixture  on 
the  rate  of  saponification  of  methyl  acetate,  which,  as  has 
already  been  pointed  out,  is  proportional  to  the  OH'  ion  con- 
centration. The  amount  of  hydrolysis  per  cent.,  IQOX,  for 
different  concentrations,  c,  of  potassium  cyanide  (mols  per  litre) 
at  25°,  determined  by  the  above  method,  is  as  follows: — 

c         .       0-947         0-235         0-095         0-024 
IQOX  .       0-31  0-72  i'i2  2-34 

K*         .  0'9  I'2  1-2  1-3  X  10— 5 

The   table   shows  that,  as  is  to  be  expected,  the  degree  of 
hydrolysis  increases  with  dilution. 


288        OUTLINES  OF  PHYSICAL  CHEMISTRY 

A  general  equation,  by  means  of  which  the  equilibrium  con- 
dition can  be  calculated  when  the  acid  and  base  are  not  neces- 
sarily present  in  equivalent  proportions,  can  readily  be  obtained 
by  applying  the  law  of  mass  action  to  the  general  equation 

B-  +  A'  +  H2O  ^  B-  +  OH'  +  HA, 

where  B-  and  A'  represent  the  positive  and  negative  ions  respec- 
tively. As  B'  occurs  on  both  sides  of  the  above  equation,  the 
latter  can  be  simplified  to 

A'  +  H2O  ^  OH'  +  HA. 

As  the  salt  and  the  base  are  practically  completely  ionised,  and 
the  acid  is  not  appreciably  ionised,  A'  and  OH'  are  proportional 
to  the  concentrations  of  salt  and  base  respectively,  and  HA  to 
that  of  the  acid.  Hence,  from  the  law  of  mass  action, 

[OH'] [HA]  _      [base][acid] 

A'          ~  [unhydrol.  salt]  ~ 

a  constant,  as  the  concentration  of  the  water  may  be  regarded 
as  constant.  K&  is  termed  the  hydrolysis  constant,  and,  like 
the  ordinary  equilibrium  constant,  is  independent  of  the  relative 
concentrations  of  the  substances  present  at  equilibrium,  but  de- 
pends on  the  temperature. 

In  order  to  illustrate  the  use  of  the  above  formula,  the  values 
of  Kfc  may  be  calculated  from  the  data  for  potassium  cyanide 
already  quoted.  In  0-095  molar  solution,  potassium  cyanide  is 
hydrolysed  to  the  extent  of  1*12  per  cent.,  hence 

O-OQS  x  i'i2 

Cbase   =   Cacid  =   -     Zi^ =  0*001064, 

and    CSait  =  0*095  ~  0-001064  =  0*094. 

(o'ooio64)(o'ooio64) 

Hence  Kh  =  ^—  -^  =  1*2  x  io~5. 

0*094 

The  values  of  the  hydrolysis  constant,  calculated  from  the 
other  observations,  are  given  in  the  table,  and  are  approxi- 
mately constant,  thus  confirming  the  above  formula.  Con- 
versely, when  from  one  set  of  observations  the  value  of 


EQUILIBRIUM  IN  ELECTROLYTES  289 

K/t  has  been  obtained,  the  degree  of  hydrolysis  at  any  other 
dilution  can  be  obtained  by  substitution  in  the  general  formula. 
For  convenience  of  calculation,  the  simple  formula  in  which 
the  acid  and  base  are  present  in  equivalent  proportions,  may 
be  written  in  the  form 


in  which  x  represents  the  proportion  of  acid  and  base  formed 
by  hydrolysis  from  i  mol  of  the  salt  and  v  is  the  dilution. 
This  form  of  the  equation  shows  at  a  glance  that  the  degree  of 
hydrolysis,  that  is,  the  value  of  x,  increases  with  dilution.  More- 
over, from  the  great  similarity  of  the  formula  (10)  to  the  dilution 
formula,  it  is  evident  that  when  the  hydrolysis  is  small  it  is 
greatly  diminished  by  the  addition  of  a  strong  base,  just  as  the 
degree  of  dissociation  of  acetic  acid  is  greatly  diminished  by  the 
addition  of  an  acetate. 

The  quantitative  relation  between  the  hydrolysis  constant, 
K^  and  the  dissociation  constants  for  the  weak  acid  and  water 
respectively  may  be  obtained  as  follows  :  The  electrolytic  dis- 
sociation of  the  acid,  HA,  is  represented  by  the  equation 

[H-][A']  =  K.  [HA]  .       .  .       (2) 

where  Kfl  is  the  dissociation  constant  of  the  acid.  In  the 
solution  there  is  the  other  equilibrium  [H*]  [OH']  =  Kw  (3) 
where  Kw  is  the  ionic  product  for  water.  Dividing  equation 
(3)  by  equation  (2)  we  obtain 

[OH']  [HA]      Kw 
"A7"       =Kl    ' 

The  left-hand  side  of  the  above  equation  is  simply  equation  (i) 
for  the  hydrolytic  equilibrium  (p.  288),  hence 

[base]  [acid]  K* 

[unhydrol.  salt]  "   Ka 

that  is,   the   hydrolysis   constant  Kh  is  the   ratio  of  the  ionic 
product  Kw  for  water  to  the  dissociation  constant  of  the  acid. 
19 


290       OUTLINES  OF  PHYSICAL  CHEMISTRY 

It  has  already  been  deduced  from  general  principles  (p.  286) 
that  the  hydrolysis  is  the  greater  the  more  nearly  the  strength 
of  water  as  an  acid  approaches  that  of  the  competing  acid,  and 
the  above  important  result  is  the  mathematical  formulation  of 
that  statement. 

In  order  to  illustrate  this  point  more  fully,  the  degree  of 
hydrolysis  of  a  few  salts  in  i/io  molar  solution  at  25°  is  given 
in  the  accompanying  table. 

Salt.  Degree  of  hydrolysis. 

Sodium  carbonate        .         .         .  3*17  per  cent. 

Sodium  phenolate         .         .         .  3  05         ,, 

Potassium  cyanide        .         .         .  1-12         „ 

Borax          .....  0^05         „ 

Sodium  acetate    ....  crooS       „ 

The  numbers  illustrate  in  a  very  striking  way  the  fact  that  only 
the  salts  of  very  weak  acids  are  appreciably  hydrolysed.  Thus 
although  acetic  acid  is  a  fairly  weak  acid  (K=r8x  io~5), 
sodium  acetate  is  only  hydrolysed  to  the  extent  of  0*008  per 
cent,  at  25°,  and  even  potassium  cyanide  is  only  hydrolysed  to 
the  amount  of  about  i  per  cent,  in  i/io  normal  solution,  although 
the  dissociation  constant  of  the  acid  is  only  1*3  x  io  ~9.  A  com- 
parison of  the  above  table  with  the  dissociation  constants  of  the 
acids  (p.  273)  is  very  instructive.  From  the  known  values  of  Ka 
and  Kw  for  hydrocyanic  acid  and  water  respectively  at  25°,  we 
have 

K«,       1-2  x  io-14 

~  =     ' 


m  very  satisfactory  agreement  with  the  observed  value  of  1*1  x 
io  ~5  (p.  288).  As  a  matter  of  fact,  however,  it  is  easier  to  deter- 
mine the  hydrolysis  constant  than  the  dissociation  constant  for 
a  very  weak  acid,  and  therefore  the  latter  is  often  calculated 
from  the  observed  value  of  the  hydrolysis  constant  by  means 
of  the  above  formula. 


EQUILIBRIUM  IN  ELECTROLYTES          291 

(b)  Hydrolysis  of  the  Salt  of  a  Weak  Base  and  a  Strong 
Acid — The  same  considerations  apply  in  this  case  as  for  the 
salt  of  a  strong  base  and  a  weak  acid.  The  general  equation 
for  the  equilibrium  is  of  the  form 

B-  +  A'  +  H2O  ^  BOH  +  H-  +  A' 
which  simplifies  to 

Applying  the  law  of  mass  action,  we  obtain 
[BOH][H-]          [base]  [acid] 

B-  "  [unhydrol.  salt] 

exactly  the  same  equation  as  is  applicable  to  the  hydrolysis  of 
he  salt  of  a  strong  base  and  a  weak  acid.  Further,  it  may  be 
shown,  by  a  method  exactly  analogous  to  that  employed  in  the 
previous  section,  that  in  this  case 

K*   =  ^~  ....       (2) 

J^6 

that  is,  the  hydrolysis  constant  Khfor  the  salt  of  a  weak  base  and 
a  strong  acid  is  the  ratio  of  the  ionic  product  for  water,  Kw,  and 
the  dissociation  constant  of  the  base,  K&. 

A  typical  case  is  the  hydrolysis  of  urea  hydrochloride,1  which 
may  be  represented  thus — 

CON2Hj  +  Cl'  +  H2O^CON2H5OH  +  H-  +  Ci: 
It  is  clear  that  the  degree  of  hydrolysis  can  at  once  be  obtained 
when  the  H*  ion  concentration  in  the  solution  has  been  deter- 
mined, and  for  this  purpose  any  of  the  methods  previously 
described  can  be  employed  (p.  275),  such  as  the  effect  on  the 
rate  of  hydrolytic  decomposition  of  cane  sugar  or  of  methyl 
acetate  or  by  electrical  conductivity  measurements.  In  the 
experiments  quoted  in  the  table,  gradually  increasing  amounts 
of  urea  were  added  to  normal  hydrochloric  acid,  and  the  H' 
ion  concentration  deduced  from  a  comparison  of  the  velocity 
constant  for  the  hydrolysis  of  cane  sugar  in  the  presence  of  the 
free  acid  (k0),  and  with  the  addition  of  urea  (/£). 

1  Walker,  Proc.  Roy.  Soc.  (Edin.),  1894,  18,  255. 


292        OUTLINES  OF  PHYSICAL  CHEMISTRY 

Normal  hydrochloric  acid  +  c  normal  urea. 


kjko 

I  -  kfko 

C  -  I  +  kjko 

c. 

k. 

=  free  HC1. 

=  salt  formed. 

=  free  urea. 

Kh. 

0 

0-00315  =k0 

I 

— 

— 

— 

o'S 

0-00237 

Q'753 

0-247 

0-253 

0-77 

I'O 

0-00184 

°'585 

0'4I5 

°'585 

0-82 

2'0 

0*00114 

0-36 

0-64 

1-36 

0-77 

4-0 

0*0006 

0-19 

0-81 

3'!9 

o'75 

On  the  assumption  that  the  rate  of  hydrolytic  decomposition 
is  proportional  to  the  H-  ion  concentration,  kjk0  represents  the 
concentration  of  the  "free"  hydrochloric  acid,  and  (i  -  kjk0) 
that  of  the  bound  acid,  which  is,  of  course,  that  of  the  unhydro- 
lysed  salt.  The  concentration  of  the  free  urea,  that  is,  of  the 
hydrolysed  salt,  is  therefore  c  —  (i  +  /£//£<,).  Substituting  in  the 
general  formula  — 

[base]  [acid]          [c-  (i  +*/&,)]  [*/*0] 
[unhydrol.  salt]  i  -  kjk0 

The  values  of  the  hydrolysis  constant  are  given  in  the  sixth 
column  of  the  table,  and  are  approximately  constant,  as  the 
theory  requires. 

The  degree  of  hydrolysis  of  a  few  salts  of  weak  bases  and 
strong  acids  in  i/io  molar  solution  at  25°  is  given  in  the  table, 
and  the  results  should  be  compared  with  the  values  for  the 
dissociation  constants  of  weak  bases  (p.  275)  in  order  to  illustrate 
equation  (2). 

Salt.  Degree  of  hydrolysis. 

Ammonium  chloride    .         .         .       0-005  Per  cent- 
Aniline  hydrochloride  .         .  1*5        „       „ 

Thiazol  hydrochloride  .         .         -19        „       „ 
Glycocoll  hydrochloride        .         .       20        „       „ 

Hydrolysis  of  the  Salt  of  a  Weak  Base  and  a  Weak 
Acid  —  The  hydrolysis  of  aniline  acetate,  a  typical  salt  of  this 
class,  is  represented  by  the  equation 
C6H5NH3-CH3COO  +  HOH^C6H5NH3OH  +  CH3COOH, 


EQUILIBRIUM  IN  ELECTROLYTES          293 

which,  on  the  assumption  that  the  salt  is  completely,  the  base 
and  acid  not  at  all,  ionised,  may  be  written  as  follows — 
C6H5NH3-  +  CH3COO'  +  HOH^C6H5NH3-  OH  +  CH3COOH. 
Applying  the  law  of  mass  action,  and  using  the  former  symbols, 
[BOH]  [HA]          [base]  [acid] 
[B-][A«]    "  "  [unhydrol.  salt]2  " 

If  we  express  the  amounts  (in  mols)  of  the  base,  acid  and 
salt  respectively  in  volume  v  of  the  solution  by  bt  a  and  s 
respectively,  the  above  equation  becomes 


that  is,  the  degree  of  hydrolysis  of  the  salt  of  a  weak  base  and  a 
weak  acid  is  independent  of  the  dilution.  Experiment  shows 
that  in  dilutions  of  12-5  and  800  litres,  aniline  acetate  is 
hydrolysed  to  the  extent  of  45-4  and  43-1  per  cent,  respectively ; 
the  slight  deviation  from  the  requirements  of  the  theory  is 
doubtless  due  to  the  fact  that  the  assumptions  made  in  deducing 
the  above  formula  are  only  approximately  true. 

Determination  of  the  Dissociation  Constant  for  Water 
— It  has  been  shown  above  that  the  process  of  hydrolysis  in 
the  case  of  a  salt  of  a  strong  base  and  a  weak  acid  may  be 
looked  upon  as  a  distribution  of  the  base  between  the  weak 
acid  and  water  acting  as  an  acid,  and  the  degree  of  hydrolysis 
therefore  depends  on  the  relative  strengths  of  the  weak  acid 
and  water.  The  relationship  between  these  three  factors  is 
expressed  by  the  equation 

[acid]  [base]      _         _  Kw 
[unhydrol.  salt]  ™      h  ~  Ka 

where  K/»  is  the  hydrolysis  constant,  Kfl  the  dissociation  con- 
stant for  the  acid,  and  Ka,  the  ionic  product  for  water.  It  is 
clear  that  if  the  degree  of  hydrolysis  of  a  salt  and  the  dissocia- 
tion constant  of  the  acid  are  known,  Kw  can  be  calculated,  and 


294        OUTLINES  OF  PHYSICAL  CHEMISTRY 

this  is  one  of  the  most  accurate  methods  for  determining  the 
degree  of  dissociation  of  water.  As  an  illustration,  we  may 
calculate  Kw  from  Shields's  value  for  the  hydrolysis  of  sodium 
acetate — 0*008  per  cent,  in  o'i  molar  solution  at  25°  (Arrhenius, 
Feb.,  1893).  We  have 

Cacid  =  Cbase  =  O'OOOoS    X    O'l, 

Csait  =  o'i  (the  amount  hydrolysed  being  negligible 
in  comparison). 

(0-00008  x  o'i)2 
Hence  v —  L  =  0*64  x  io~9  =  K/,. 

O'l 

Now  Kw  =  KhKa  =  (0-64  x  io~9)  x  (r8  x  lo"5)  =  ri6  x  io~14. 

Since  [H'][OH'J  is  thus  found  to  be  approximately  1*2  x 
io~14,  the  concentration  of  H'  or  OH'  ions  (mols  per  litre)  in 
water  at  25°  is  i'i  x  io~7. 

KK,  can  also  be  calculated  from  measurements  of  the  hydro- 
lysis of  salts  of  strong  acids  and  weak  bases,  and,  perhaps  with 
still  greater  accuracy,  from  measurements  with  salts  of  weak 
acids  and  weak  bases.1 

The  degree  of  dissociation  of  water  has  been  determined  by 
three  other  methods  at  25°  with  the  following  results  : — 

E.M.F.  of  hydrogen-oxygen  cell  (Ostwald,  January, 
1893)  (corrected  value),  i'o  x  10  ~  7  at  25°. 

Velocity  of  hydrolysis  of  methyl  acetate  (Van't  Hoff- 
Wijs,  March,  1893),  1*2  x  10  ~  7  at  25°. 

Conductivity  of  purest  water  (Kohlrausch,  1894), 
ro5  x  10  "  7  at  25°. 

When  it  is  borne  in  mind  how  small  the  dissociation  is,  the 
close  agreement  in  the  values  obtained  by  these  four  inde- 
pendent methods  is  very  striking,  and  forms  a  strong  justifica- 
tion for  the  original  assumption  that  water  is  split  up  to  an 
extremely  small  extent  into  ions. 

The  question  can  be  still  further  tested  by  applying   van't 

1  Lunden,  J.  Chim.  Phys.,  1907,  5,  574  ;  Kanolt,  y.  Amer.  Chem.  Soc., 
1907,  29,  1402.  For  salts  of  weak  bases  and  weak  acids  the  formula  Kh  = 
[Ka  K&J/Kw  applies. 


EQUILIBRIUM  IN  ELECTROLYTES  295 

Hoff  s  equation  connecting  heat  development  and  displacement 
of  equilibrium  to  the  equilibrium  between  water  and  its  ions. 
For  the  degree  of  dissociation  at  different  temperatures,  the 
following  values  were  obtained  by  Kohlrausch  from  conduc- 
tivity measurements  :  — 

Temperature        .         .      o°      2°      10°     15°    26°    34°    42°          50° 
Degree  of  dissociation     0*35    0-39   0-56   0-8    rog    1-47    1-93    2*48  x  io~7 

From  any  two  of  these  measurements  the  heat  development,  Q, 
of  the  reaction,  H2O  ;±  H-  +  OH',  can  be  calculated  by  sub- 
stitution in  the  general  formula  (p.  167). 


From  the  values  l  of  K  at  o°  and  50°,  Q  =  -  13,740  cal.,  and 
from  that  at  2°  and  42°,  Q  =  -  13,780  cal. 

In  a  previous  section  (p.  284)  it  has  been  pointed  out  that, 
according  to  the  electrolyte  dissociation  theory,  the  neutraliza- 
tion of  a  strong  base  by  a  strong  acid  consists  essentially  in  the 
combination  of  H-  and  OH'  ions  to  form  water.  The  heat 
given  out  in  the  reaction  is  about  13,700  cal.  for  molar  quanti- 
ties, in  excellent  agreement  with  the  above  value.  This  sup- 
ports the  assumption  that  the  variation  of  the  conductivity  of 
pure  water  with  dilution  is  due  to  the  displacement  of  the 
equilibrium  H-  +  OH'  ^±H2O,  in  the  direction  indicated  by 
the  lower  arrow.  The  value  of  Q,  obtained  directly  as  above, 
may  be  termed  the  heat  of  ionisation  of  water  ;  it  is  the  heat 
given  out  when  i  mbl  of  H-  and  OH'  ions  combine  to  form 
water. 

The  heat  of  ionisation  of  any  electrolyte  can  naturally  be 
calculated  in  the  same  way  from  the  displacement  of  the  equili- 
brium with  temperature.  The  effect  of  increased  temperature 
on  the  degree  of  ionisation  is  almost  always  slight,  and  in  the 
majority  of  cases  the  ionisation  is  slightly  diminished.  As  an 
illustration,  the  degree  of  electrolytic  dissociation  for  i/io  molar 
sodium  chloride  over  a  wide  range  of  temperature,  as  deter- 

1  K2  =  (2-48  x  io-7)2  at  50°  ;  Kj  =  (0-35  x  io-7)2  at  o°  (p.  283). 


-  296       OUTLINES  OF  PHYSICAL  CHEMISTRY 

mined  by  Noyes  and  Coolidge,1  may  be  quoted.  The  values 
obtained  were  84  per  cent,  at  18°,  79  per  cent,  at  140°,  74  per 
cent,  at  218°,  67  per  cent,  at  281°,  and  60  per  cent,  at  306°. 
Corresponding  with  the  small  variation  in  the  degree  of  ionisa- 
tion  with  temperature,  the  heat  of  ionisation  is  small,  and  may 
be  positive  (as  in  the  present  case)  or  negative. 

Theory  of  Indicators — The  indicators  used  in  acidimetry 
and  alkalimetry  have  the  property  of  giving  different  colours 
depending  on  whether  the  solution  is  acid  or  alkaline.  Ac- 
cording to  Ostwald's  theory,  which  has  met  with  fairly  general 
acceptance,  such  indicators,  including  methyl-orange,  phenol- 
phthalein  and  /-nitrophenol,  are  weak  electrolytes,  and  their 
use  depends  on  the  fact  that  the  ions  and  the  non-ionised  com- 
pounds have  different  colours.  Since  salts  are  almost  always 
highly  ionised,  it  is  clear  that  only  weak  acids  and  bases  can 
be  employed  as  indicators. 

Phenolphthalein  is  a  very  weak  acid,  the  non-ionised  acid  is 
colourless,  and  the  negative  ion  red.  In  aqueous  solution  it  is 
ionised  according  to  the  equation 

HP^H-  +  P'(red) 

(where  P'  is  the  negative  ion),  but  so  slightly  that  the  solution  is 
practically  colourless.  If  now  sodium  hydroxide  is  added,  the 
highly-dissociated  sodium  salt  is  formed,  and  the  solution  is 
deeply  coloured  owing  to  the  presence  of  the  red  anion,  P'. 
If,  on  the  other  hand,  the  solution  -contains  a  slight  excess  of 
acid,  the  increased  H'  ion  concentration  drives  back  the  ioni- 
sation of  the  phenolphthalein  in  the  direction  indicated  by  the 
lower  arrow,  and  the  solution  becomes  colourless  (cf.  p.  277). 
Finally,  if  a  weak  base,  such  as  ammonium  hydroxide,  is  added, 
the  ammonium  salt  will  be  partly  hydrolysed,  according  to  the 
equation 

NH4P  +  HOH^NH4OH  +  HP, 
and  excess  of  the  base  will  be  required  in  order  to  drive  back 

1  Zeitsch.  Physikal  Chem.,  1904,  46,  323. 


EQUILIBRIUM  IN  ELECTROLYTES 


297 


the  hydrolysis  (p.  289) ;  in  other  words,  there  will  not  be  a  sharp 
change  of  colour  when  ammonium  hydroxide  is  added. 

Methyl-orange  is  an  acid  of  medium  strength,  the  non-ionised 
acid  is  red,  the  negative  ion  yellow.     As  the  acid  is  ionised  in 
aqueous  solution  to  some  extent,  according  to  the  equation 
HM  (red)  ^  H-  +  M'  (yellow), 

the  solution  shows  a  mixed  colour.  The  effect  of  the  addition 
of  acids  and  alkalis  is  similar  to  that  on  phenolphthalein,  and 
only  differs  in  degree.  Since  the  aqueous  solution  already  con- 
tains a  considerable  proportion  of  H'  ions,  it  is  evident,  from 
the  considerations  advanced  on  p.  276,  that  a  considerable 
excess  will  be  required  to  drive  back  the  dissociation  in  the 
direction  indicated  by  the  lower  arrow,  so  as  to  turn  the  solu- 
tion red.  The  proportion  of  H*  ions  in  such  a  weak  acid  as 
acetic  acid  is  not  sufficient  for  this  purpose,  and  therefore 
methyl-orange  should  not  be  employed  as  an  indicator  for 
weak  acids.  It  is,  on  the  other  hand,  a  suitable  indicator  for 
weak  bases,  such  as  ammonia,  as  the  salt  formed  is  much  less 
hydrolysed  than  the  corresponding  phenolphthalein  salt,  and 
therefore  the  change  of  colour  is  sharper. 

Basic  indicators  are  not  in  use. 

The  considerations  to  be  borne  in  mind  in  selecting  an 
indicator,  or  in  choosing  a  suitable  alkali  for  titrating  an  acid, 
or  vice  versa,  may  be  put  concisely  as  follows  (Abegg)  : — 


Solutions  used. 

... 

P         i 

Acid. 

Base. 

Strong 

Strong 

Any 

Any 

Strong 

Weak 

Strong  acid 

Methyl-orange,  /-nitrophenol 

Weak 
Weak 

Strong 
Weak 

Weak  acid 
None  satisfactory 

Phenolphthalein,  litmus 
Should  be  avoided 

Some  investigators  maintain  that  the  ionisation  theory  does 
not  give  a  satisfactory  representation  of  the  behaviour  of  indi- 


298       OUTLINES   OF  PHYSICAL  CHEMISTRY 

cators,  but  that  the  changes  of  colour  are  due  to  changes  of 
constitution,  usually  from  the  benzenoid  to  the  quinonoid  type 
and  vice  versa.1  In  an  aqueous  solution  of  phenolphthalein,  for 
instance,  there  are  only  traces  of  the  quinonoid  (coloured)  modifi- 
cation, and  the  solution  is  colourless,  but  on  the  addition  of 
alkali  the  phenolphthalein  salt  is  formed,  the  negative  ions  of 
which,  being  of  the  quinonoid  type,  are  strongly  coloured. 

The  Solubility  Product — We  have  now  to  consider  an 
equilibrium  of  rather  a  different  type — in  which  the  solution 
is  saturated  with  regard  to  the  electrolyte.  In  such  a  case 
there  is  equilibrium  between  the  solid  salt  and  the  non-ionised 
salt  in  the  solution,  so  that  the  concentration  of  the  non-ionised 
salt  remains  constant  at  constant  temperature.  Further,  there 
is  equilibrium  in  the  solution  between  the  non-ionised  salt  and 
its  ions,  which  may  be  represented,  in  the  case  of  silver  chloride, 
for  example,  by  the  equation  Ag-  +  Cl'^AgCl.  Applying 
the  law  of  mass  action,  we  have,  for  the  latter  equilibrium, 

[Ag-][Cl']  =  K[AgCl]  =  S, 

where  S  is  the  product  of  the  concentrations  of  the  two  ions 
— the  so-called  solubility  product — and  is  constant,  since  the 
right-hand  side  of  the  above  equation  is  constant.  The  equi- 
libria in  the  heterogeneous  system  may  be  represented  as 
follows  : — 

Ag-  +  Cr  ;±  AgCl  (in  solution) 

*  t 
AgCl  (solid). 

As  will  be  shown  later,  the  solubility  product  for  silver  chloride 
at  25°  is  1-56  x  io-10,  when  the  ionic  concentrations  are  ex- 
pressed in  mols  per  litre.  If  the  solution  has  been  prepared 
by  dissolving  the  salt  in  water,  the  ions  are  necessarily  present 
in  equivalent  proportions,  so  that  a  solution  of  silver  chloride, 
saturated  at  25°,  contains  vi'56  x  io~10  =  1*25  x  io~5  mols 
of  Ag-  and  of  Cl'  ions. 

The  ions  need  not,  however,  be  present  in  equivalent  propor- 
1  C/.  Hewitt,  Analyst,  1908,  33,  85. 


EQUILIBRIUM  IN   ELECTROLYTES 


299 


tions ;  if  by  any  means  the  solubility  product  is  exceeded,  for 
example,  by  adding  a  salt  with  an  ion  in  common  with  the 
electrolyte,  the  ions  unite  to  form  undissociated  salt,  which  falls 
out  of  solution,  and  this  goes  on  till  the  normal  value  of  the 
solubility  product  is  reached.  Perhaps  the  best-known  illustra- 
tion of  this  is  the  precipitation  of  sodium  chloride  from  its 
saturated  solution  by  passing  in  gaseous  hydrogen  chloride. 
In  this  case  the  original  equilibrium  between  equivalent  amounts 
of  Na'  and  Cl'  ions  is  disturbed  by  the  addition  of  a  large 
excess  of  Cl'  ions,  and  sodium  chloride  is  precipitated  till  the 
original  solubility  product  is  regained,  when  the  solution  con- 
tains an  excess  of  Cl'  ions  and  relatively  few  Na'  ions. 

As  already  mentioned,  the  difference  between  the  present 
form  of  equilibrium  and  those  previously  considered  is  that  the 
concentration  of  the  non-ionised  salt  in  the  solution  is  constant 
at  constant  temperature.  If  it  is  diminished  in  any  way,  salt 
is  dissolved  till  the  original  value  is  reached  ;  if  it  is  exceeded, 
as  in  the  case  just  mentioned,  salt  falls  out  of  solution  till  the 
original  value  is  reached. 

Since  the  equilibrium  equation  for  a  binary  salt  is  symmetrical 
with  regard  to  the  two  ions,  it  follows  that  the  solubility  of  such  a 
salt  should  be  depressed  to  the  same  extent  by  the  addition  of 
equivalent  amounts  of  its  common  ions,  whether  positive  or 
negative.  This  consequence  of  the  theory  was  tested  by  Noyes, 
who  determined  the  influence  of  the  addition  of  equivalent 
amounts  of  hydrochloric  acid  and  of  thallous  nitrate  on  the 
solubility  of  thallous  chloride,  with  the  following  results  : — 

Solubility  of  thallous  chloride  at  25° : — 


Concentration  of 
Substance  added 
(mols  per  litre). 

T1NO3  added. 

HC1  added. 

O 
0*0283 
0-147 

o'oi6i 
0*0084 
0*0032 

0*0161 
0*0083 
0-0033 

300       OUTLINES  OF  PHYSICAL  CHEMISTRY 

The  figures  in  the  first  column  show  the  amounts  of  thallous 
nitrate  and  of  hydrochloric  acid  added,  those  in  the  second  and 
third  columns  represent  the  solubility  of  thallous  chloride  in 
mols  per  litre.  The  results  show  that  the  requirements  of 
the  theory  are  satisfactorily  fulfilled. 

The  above  results  hold  independently  of  the  relative  amounts 
of  ions  and  non-ionised  salt  in  the  solution.  Since  in  dilute 
solution  all  salts  are  highly  ionised,  it  may,  however,  be  as- 
sumed that  difficultly  soluble  salts,  such  as  silver  chloride,  are 
almost  completely  ionised  in  solution  ;  in  other  words,  the  con- 
centration of  non-ionised  salt  in  solution  may  be  regarded  as 
negligible  in  comparison  with  that  of  the  ions.  This  deduction 
is  of  great  importance  in  estimating  the  solubility  of  difficultly 
soluble  salts  (see  next  page). 

Applications  to  Analytical  Chemistry — The  above  con- 
siderations with  regard  to  the  solubility  product  are  of  the 
greatest  importance  for  analytical  chemistry.  A  precipitate  can 
only  be  formed  when  the  product  of  the  ionic  concentrations 
attains  the  value  of  the  solubility  product,  which  for  every  salt 
has  a  definite  value  depending  only  on  the  temperature.  For 
example,  magnesium  hydroxide  is  precipitated  from  solutions  of 
magnesium  salts  by  ammonia  because  the  solubility  product 
[Mg-]  [OH'] 2  is  exceeded.  When,  however,  ammonium  chloride 
is  previously  added  in  excess  to  the  hydroxide,  the  OH'  ion 
concentration  is  diminished  to  such  an  extent  (p.  277)  that  the 
solubility  product  is  not  reached,  and  precipitation  no  longer 
occurs.  Similarly,  zinc  sulphide  is  precipitated  when  the 
product  [Zn"][S"]  exceeds  a  certain  value.  In  alkaline  solu- 
tion, an  extremely  small  concentration  of  hydrogen  sulphide 
suffices  for  this  purpose,  as  the  sulphide  is  considerably  ionised, 
but  in  acid  solution  the  depression  of  the  ionisation  of  the 
hydrogen  sulphide,  in  other  words,  the  diminution  in  the  con- 
centration of  S"  ions,  is  so  great  that  the  solubility  product  is 
not  reached.  On  the  other  hand,  the  solubility  product  for 
certain  heavy  metals,  such  as  lead,  copper,  and  bismuth,  is  so 


EQUILIBRIUM  IN  ELECTROLYTES  301 

small  that  it  is  reached  even  in  acid  solution.  It  is,  however, 
possible  to  increase  the  acid  concentration  (and  therefore  to 
diminish  the  S"  ion  concentration)  to  such  an  extent  that  the 
ionic  product  is  not  reached  even  for  some  of  the  above  metals, 
for  example,  lead  sulphide  in  concentrated  hydrochloric  acid  is 
not  precipitated  by  a  current  of  hydrogen  sulphide. 

On  the  same  basis,  a  fact  which  has  long  been  familiar  in 
quantitative  analysis,  that  precipitation  is  more  complete  when 
excess  of  the  precipitant  is  added,  can  readily  be  accounted  for. 
A  saturated  aqueous  solution  of  silver  chloride  contains  about 
1*25  x  io~5  gram  equivalents  of  the  salt  per  litre,  and  the  ad- 
dition of  ten  times  that  concentration  of  Cl'  ions  (added  in  the 
form  of  sodium  chloride)  will  diminish  the  amount  of  silver  in 
solution  to  about  i/io  of  its  original  value  (on  the  assumption 
that  the  concentration  of  the  non-ionised  salt  is  negligible  in 
comparison  with  that  of  the  ions)  (cf.  p.  277).  It  is  thus  evident 
that  in  the  gravimetric  estimation  of  combined  chlorine  as  silver 
chloride  there  might  be  considerable  error  owing  to  the  solubility 
of  silver  chloride  in  water,  but  if  a  fair  excess  of  the  precipitant 
is  used,  the  error  is  quite  negligible. 

The  concentration  in  saturated  solution  at  25°,  and  the 
solubility  product  of  a  few  difficultly  soluble  salts  are  given  in 
the  accompanying  table. 

Salt.  Saturation  Concentration  Solubility  Product 

(mols  per  litre).  (mols  per  litre). 

Silver  chloride       Ag-  =  1-25  x  io~5  1-56  x  io~10 

„     bromide        ,,     =  6*6  x  io"7  4*35  x  io~13 

„     iodide            „     =  i'o  x  io~8  1*0     x  io~16 

Thallous  chloride  Tl-   =  1-6  x  lo'2  2-6     x  io~  * 

Cuprous  chloride  Cu'  =  i'i  x  io~3  1-2     x  io~  6 

Lead  sulphide       Phr  =  5*1  x  io~8  2'6     x  io-15 

Copper  sulphide  Cu"  =  i-i  x  io~21  1-2     x  io~42 

Experimental  Determination  of  the  Solubility  of  Diffi- 
cultly Soluble  Salts— When  a  saturated  solution  of  a  rela- 


302        OUTLINES  OF  PHYSICAL  CHEMISTRY 

tively  insoluble  salt  is  so  dilute  that  complete  ionisation  may  be 
assumed  (p,v  =  p^ ),  the  solubility  of  the  salt  may  readily  be 
obtained  from  electrical  conductivity  measurements.  The 
molecular  conductivity  at  infinite  dilution,  /^  ,  can  be  obtained 
indirectly  (p.  258),  the  specific  conductivity  of  the  saturated 
solution  is  determined  in  the  usual  way,  and,  by  substitution  in 
the  formula  /x^  =  KV,  we  obtain  the  value  of  v,  that  is,  the 
volume  in  c.c.,  in  which  a  mol  of  the  substance  is  dissolved.  If 
the  solubility  is  required  in  mols  per  litre,  then 

v  =  1000  V,  and 
/*  ^  =  1000  KV, 

where  V  is  the  volume  in  litres  in  which  a  mol  of  the  sub- 
stance is  dissolved.  As  the  specific  conductivity  of  such  a 
solution  is  small,  the  conductivity  of  the  water  becomes  of 
importance,  and  it  is  necessary  to  subtract  from  the  observed 
specific  conductivity  of  the  solution  the  conductivity  of  the 
water,  determined  directly.  For  such  measurements,  "con- 
ductivity "  water,  of  a  specific  resistance  not  much  less  than 
io6  ohms,  should  be  used. 

As  an  example  of  the  determination  of  solubilities  by  this 
method,  Bottger  found  that  a  solution  of  silver  chloride  saturated 
at  20°  had  K  =  1*33  x  io  ~6  after  subtracting  the  specific  con- 
ductivity of  the  water.  Hence,  as  //^  for  silver  chloride  at  20°, 
determined  indirectly  (p.  258),  is  125-5,  we  obtain,  by  substitu- 
tion in  the  above  formula, 

125-5  =  1000  x  1-33  x  io~6V, 

and  V  =  — LJLs =  94,400, 

1-33  x  io- 

that  is,  94,400  litres  of  a  solution  of  silver  chloride,  saturated 
at  20°,  contain  i  mol  of  the  salt.  In  one  litre  of  solution  there 
is,  therefore,  1/94,400  =  1-06  x  io~5  mol,  or  0-00152  grams 
of  silver  chloride.  The  values  for  the  solubility  of  a  number  of 
difficultly  soluble  salts  obtained  by  this  method  are  given  in 
the  previous  section  (p.  301). 


EQUILIBRIUM  IN  ELECTROLYTES  303 

Complex  Ions — Complex  ions  have  already  been  defined  as 
being  formed  by  association  of  ions  with  non-ionised  molecules 
It  is  well  known  that  though  silver  halogen  salts  are  only 
slightly  soluble  in  water  they  are  readily  soluble  in  the  presence 
of  ammonia.  This  phenomenon  is  due  to  the  formation  of 
complex  ions  (p.  281),  in  which  the  Ag-  ions  are  associated 
with  ammonia  molecules,  forming  univalent  ions  of  the  type 
Ag(NH3)*.  As  nearly  all  the  silver  is  present  in  this  form 
and  very  little  in  the  form  of  Ag-  ions,  it  is  evident  that  a 
solution  may  contain  a  very  considerable  amount  of  a  silver  salt 
before  the  solubility  product  [Ag-]  [X']  is  reached. 

The  determination  of  the  exact  composition  of  the  complex 
ions  in  a  solution  is  sometimes  a  matter  of  difficulty,  but  the 
law  of  mass  action  is  often  of  great  assistance  in  this  respect. 
If,  for  example,  the  solution  of  a  silver  salt  in  ammonia 
contains  mainly  complex  ions  of  the  formula  Ag(NH8)-f 
there  must  be  an  equilibrium  represented  by  the  equation 
Ag(NH3)2  ;rt  Ag-  +  2NH3,  and  by  the  law  of  mass  action  the 

expression  ~1UL  TT  . 3-*     must  be  constant.    To  test  this  point 
Ag(NH3)- 

the  concentrations  of  the  ammonia  and  of  the  silver  ions  were 
systematically  varied,  and  it  was  found  that  the  above  expres- 
sion remained  constant,  thus  showing  that  the  assumption  as 
to  the  composition  of  the  complex  ions  is  correct.  The  azure 
blue  solutions  obtained  by  adding  ammonia  in  excess  to  solu- 
tions of  cupric  salts  appear  from  the  results  of  distribution  (p. 
178)  and  optical  measurements  to  contain  the  copper  exclusively 
as  Cu(NH3)4"  ions.  The  solutions  obtained  by  the  action  of 
ammonia  on  cobalt  and  chromium  salts  have  been  thoroughly 
investigated  by  Werner : l  they  contain  complex  ions  of  the 
formulae  Co(NH3)6-  and  Cr(NH3)fl-. 

Other  compounds  besides  ammonia  can  become  associated 
with  positive  ions  to  form   complex  cations.      For  example, 
Werner  has   shown    that  the  ammonia  groups   in   the   com- 
plex cobalt  ions  mentioned   above   can   be  successively  dis- 
1  Summary,  Anorganische  Chemie,  2nd  edition,  Brunswick,  1909. 


304        OUTLINES  OF  PHYSICAL  CHEMISTRY 

placed  by  water  molecules,  forming  compounds  of  the  type 
[Co(NH8)5H20]-,  [Co(NH3)4(H20)2]-     .       .       . 

and  finally 

[Co(H20)6]- 

It  is  probable  that  in  the  aqueous  solutions  of  many  salts  com- 
plex ions  containing  water  are  present. 

Complex  anions,  formed  by  the  association  of  negative  ions 
with  neutral  molecules,  are  also  known.  Solutions  of  cadmium 
iodide  contain  CdI4"  ions  (p.  281),  and  the  solution  obtained  by 
the  addition  of  excess  of  potassium  cyanide  to  solutions  of  silver 
salts  contains  potassium  silver  cyanide,  KAg(CN)2,  which  is 
largely  ionised  according  to  the  equation 


Influence  of  Substitution  on  Degree  of  lonisation— 

Reference  has  already  been  made  to  the  influence  of  substitu- 
tion on  the  strength  of  acids.     As  the  effect  of  substitution  on 
the  degree  of  ionisation  has  been  most  extensively  investigated 
for  this  class  of  compound,  a  few  further  examples  may  be 
given.     In  the  accompanying  table,  the  affinity  or  dissociation 
constants  for  some  mono-substituted  acetic  acids  are  given,  the 
value  of  K  holding  for  25°  (concentrations  in  mols  per  litre). 
Acetic  acid  CH8COO;H  .        .         .         .     0-000018 
Propionic  acid  CH3CH2COO'H       .         .     0-000013 
Chloroacetic  acid  CH2C1COO'H      .         .     0*00155 
Bromoacetic  acid  CH2BrCOO'H     .         .     0*00138 
Cyanacetic  acid  CH2CNCOO*H      .         .     0-00370 
Glycollic  acid  CH2OHCOO'H         .         .     0-000152 
Phenylacetic  acid  C6H5CH2COO'H          .     0-000056 
Amidoacetic  acid  CH2NH2COO'H  .     3-4  x  10  ~  10 

As  the  carboxyl  group  only  is  concerned  directly  in  ionisation, 
the  above  table  affords  an  excellent  illustration  of  the  influence 
of  a  group  on  a  neighbouring  one.  The  table  shows  that  when 
one  of  the  alkyl  hydrogens  in  acetic  acid  is  displaced  by 
Cl,  Br,  CN  or  OH  or  C6H5  an  increase  in  the  activity  of  the 


EQUILIBRIUM  IN  ELECTROLYTES  305 

acid  is  brought  about ;  the  effect  is  least  for  the  phenyl  group 
and  greatest  for  the  cyanogen  group.  On  the  other  hand,  the 
methyl  group  (in  propionic  acid)  diminishes  the  activity  slightly, 
and  the  amido  group  diminishes  it  enormously. 

These  .observations  can  readily  be  accounted  for1  on  the 
assumption  that  the  atoms  or  groups  take  their  ion-forming 
character  into  combination.  Thus  the  Cl,  Br,  CN  and  OH 
groups,  which  tend  to  form  negative  ions,  increase  the  tendency 
of  the  groups  into  which  they  enter  to  form  negative  ions. 
The  "  negative  favouring "  character  of  the  phenyl  group  is 
slight  but  distinct.  On  the  other  hand,  the  so-called  basic 
groups,  such  as  NH2,  lessen  the  tendency  of  the  group  into 
which  they  enter  to  form  negative  ions,  as  is  very  strikingly 
shown  in  the  case  of  amidoacetic  acid.  The  methyl  group  has 
also  a  slight  diminishing  effect  on  the  tendency  of  a  group  to 
form  negative  ions. 

The  magnitude  of  the  influence  of  a  substituent  on  a  particu- 
lar group  depends  on  its  distance  from  that  group.  This  is 
very  well  shown  by  the  influence  of  the  hydroxyl  group  on  the 
affinity  constant  of  propionic  acid. 

Propionic  acid  CH3CH2COO"H   .         .         .     0-0000134 
Lactic  acid  CH3CHOHCOO'H  .         .     0-000138 

/3-oxypropionic  acid  CH2OHCH2COO'H      .     0-0000311 

When  the  OH  group  is  in  the  a  (neighbouring)  position  its 
effect  on  the  dissociation  constant  is  more  than  four  times  as 
great  as  when  it  is  in  the  /?  position. 

It  seems  plausible  to  suppose  that  a  comparison  of  the 
influence  of  groups  in  the  ortho,  meta  and  para  positions  on  the 
carboxyl  group  of  benzoic  acid  might  throw  some  light  on  the 
question  of  the  relative  distances  between  the  groups  in  the 
benzene  nucleus.  The  dissociation  constants  of  benzoic  acid 
and  the  three  chlor-substituted  acids  are  as  follows : — 

1  A  complete  theory  of  the  phenomena  in  question  has  recently  been 
worked  out  by  Flurscheim  (Trans.  Chem.  Soc.t  1909,  95,  718;  Proc.,  1909, 
193). 

2O 


306       OUTLINES  OF  PHYSICAL  CHEMISTRY 

Benzoic  acid  C6H5COOH       .         .  .     0*000060 

o-  Chlorobenzoic  acid  C6H4C1COOH  .  .     0*00132 
m-             „               „                „  0*000155 

p-  »>  >»  »  0*000093 

It  will  be  observed  that  the  presence  of  the  halogen  in  the  ortho 
position  greatly  increases  the  strength  of  the  acid,  and  it  is  a 
general  rule  that  the  influence  of  substituents  is  always  greatest 
in  this  position.  The  effect  of  substituting  groups  in  the  meta 
and/ara  positions  is  much  smaller,  and  the  order  of  the  two  is 
not  always  the  same.  As  the  table  shows,  w-chlorobenzoic 
acid  is  rather  stronger  than  the  para  acid,  but  on  the  other  hand 
/-nitrobenzoic  acid  is  somewhat  stronger  than  the  meta  acid. 

Similar  considerations  apply  to  the  influence  of  substituents 
on  the  strength  of  bases,  but,  as  is  to  be  expected,  the  effect  of 
the  various  groups  is  exerted  in  the  opposite  direction  to  that  on 
acids.  Thus  the  displacement  of  a  hydrogen  atom  in  ammonium 
hydroxide  by  the  methyl  group  gives  a  stronger  base  (methyl 
amine)  but  the  entrance  of  a  phenyl  group  gives  a  much  weaker 
base  (aniline)  (cf.  p.  275). 

Reactivity  of  the  Ions — It  is  a  well-known  fact  in  qualita- 
tive analysis  that  in  the  great  majority  of  cases  the  positive 
component  of  a  salt  (e.g.,  the  metal)  answers  certain  tests,  quite 
independently  of  the  nature  of  the  acid  with  which  it  is  combined, 
and  in  the  same  way  acids  have  certain  characteristic  reactions, 
independent  of  the  nature  of  the  base  present.  These  facts  are 
plausibly  accounted  for  on  the  electrolytic  dissociation  theory 
by*  assuming  that  the  positive  and  negative  parts  of  the  salts 
(the  ions)  exist  to  a  great  extent  independently  in  solution,  and 
that  the  well-known  tests  for  acids  and  bases  are  really  tests  for 
the  free  ions.  Thus  silver  nitrate  is  not  a  general  test  for 
chlorine  in  combination,  but  only  for  chlorine  ions.  It  is  well 
known  that  potassium  chlorate  gives  no  precipitate  with  silver 
nitrate,  although  it  contains  chlorine  ;  this  is  readily  accounted 
for  on  the  electrolytic  dissociation  theory  because  the  solution 
of  the  salt  contains  no  Cl'  ions,  but  only  C1O3'  ions,  which  give 


EQUILIBRIUM  IN  ELECTROLYTES  307 

their  own  characteristic  reactions.  These  views  appear  still 
more  plausible  when  cases  are  considered  in  which  the  usual 
tests  fail,  for  example,  mercuric  cyanide  does  not  give  all  the 
ordinary  reactions  for  mercury.  This  could  be  accounted  foi 
by  supposing  that  the  compound  is  not  appreciably  ionised  in 
solution,  so  that  practically  no  Hg"  ions  are  present,  and  as  a 
matter  of  fact  the  aqueous  solution  of  mercuric  cyanide  is 
practically  a  non-conductor. 

The  chief  characteristic  of  ionic  reactions  is  their  great  rapidity ; 
they  are  for  all  practical  purposes  instantaneous,  and  it  is  doubt- 
ful if  the  speed  of  a  purely  ionic  reaction  has  so  far  been 
measured.  It  is  well  known  that  silver  nitrate  reacts  with  the 
chlorine  in  organic  compounds  such  as  ethyl  chloride  and  chlor- 
acetic  acid,  but  very  slowly  as  compared  with  its  action  on 
sodium  chloride.  There  is  good  reason  for  supposing  that  the 
reactions  last  mentioned  are  not  ionic  actions,  but  that  the 
changes  take  place  between  the  silver  salt  and  combined  chlorine. 

The  great  reactivity  of  the  ions  in  cases  where  it  is  known 
that  they  are  actually  present  has  led  Euler  and  others  to 
postulate  that  all  reactions  are  ionic,  and  that  in  very  slow 
reactions  we  are  dealing  with  excessively  small  ionic  concen- 
trations.1 This  question  cannot  be  adequately  considered  here, 
but  it  may  be  mentioned  that  the  available  experimental  evi- 
dence does  not  seem  to  lend  any  support  to  Euler's  theory. 
There  is  good  reason  to  suppose  that  chemical  reactions  may 
take  place  between  non-ionised  molecules  as  well  as  between 
ions. 

Practical  Illustrations.  Dilution  Law.  Conductivity  of 
Acids  and  Salts — Many  of  the  results  discussed  in  this  chapter 
can  be  conveniently  illustrated  by  means  of  the  apparatus2 
shown  in  Fig.  36.  The  glass  vessels  each  contain  two  circular 
electrodes  of  platinized  platinum,  the  lower  one  is  connected 
with  a  wire  which  passes  through  the  bottom  of  the  vessel 
and  is  connected  through  a  lamp  to  the  wire  E.  The  upper 
electrode,  which  is  movable,  is  connected  to  a  wire  which 

1  Compare  Arrhenius,  Electrochemistry  (English  Edition),  p.  180. 
2Noyes  and  Blanchard,  J.  Amer.  Chem.  Soc.,  1900,  22,  726. 


3o8        OUTLINES  OF  PHYSICAL  CHEMISTRY 


passes  through  the  cork  loosely  closing  the  vessel,  and  is 
connected  to  the  upper  wire  F.  The  electrodes  in  each 
vessel  should  be  of  approximately  the  same  cross-section,  and 
the  four  lamps  of  equal  resistance.  The  wires  E  and  F  are 
connected  to  the  terminals  of  a  source  of  alternating  current, 
and  as  they  are  at  constant  potential  throughout,  the  fall  of 
potential  through  each  of  the  vessels  from  E  to  F  must  be 
the  same  when  a  current  is  passing. 


FIG.  36. 

The  use  of  the  arrangement  may  be  illustrated  by  employing 
it  to  prove  the  dilution  law  in  the  form  a  =  »Jkv.  Solutions  of 
monochloracetic  acid  containing  i  mol  of  the  salt  in  i,  4  and 
1 6  litres  respectively  are  prepared,  and  the  vessels  A,  B  and  C 
nearly  filled  with  them.  When  connection  is  made  with  the 
alternating  current,  it  will  be  found  that  the  brightness  of  the 
lamps  is  very  different,  but  the  positions  of  the  upper  electrodes 
can  be  so  adjusted  that  the  lamps  are  equally  bright.  Under 


EQUILIBRIUM  IN  ELECTROLYTES  309 

these  circumstances  it  is  evident  that  the  resistance  of  each 
solution  is  the  same.  On  measuring  the  distances  between  the 
electrodes,  it  will  be  found  that  for  the  solutions  v  —  i,  v  =  4, 
v  =  1 6,  the  distances  are  in  the  ratio  4:2:1.  Hence,  as 
the  conductivities  are  inversely  proportional  to  the  distances 
between  the  electrodes,  aoc  \]v. 

Further,  it  may  be  shown  that,  although  acids  differ  very 
greatly  in  conductivity,  neutral  salts,  even  of  weak  acids,  have 
a  conductivity  nearly  as  great  as  that  of  strong  acids.  The 
vessels  are  filled  with  1/4  normal  solutions  of  hydrochloric  acid, 
sulphuric  acid,  monochloracetic  acid  and  acetic  acid  respectively, 
and  when  the  distances  are  altered  till  the  lamps  are  equally 
bright,  it  will  be  found  that  tha  electrodes  are  very  near  in  the 
acetic  acid  solution,  far  apart  in  the  hydrochloric  acid  solution, 
and  at  intermediate  distances  for  the  other  two  acids.  Sufficient 
sodium  hydroxide  to  neutralize  the  acid  is  now  added  to  each 
vessel,  and  after  stirring  and  again  adjusting  to  equal  brightness 
of  the  lamps,  it  will  be  found  that  the  distances  for  all  four 
solutions  are  approximately  equal. 

Eqtiilibrium  Relations  as  shown  by  Indicators — The  equi- 
librium relations  in  the  case  of  weak  acids  and  bases  may 
be  shown  very  well  by  means  of  indicators.  Each  of  two 
beakers  contains  100  c.c.  of  water,  i  c.c.  of  n/i  sodium 
hydroxide,  and  a  few  drops  of  methyl-orange.  To  the  con- 
tents of  one  beaker  n  hydrochloric  acid  is  added  drop  by 
drop  by  means  of  a  pipette,  and  to  the  other  n  acetic  acid 
is  added  in  the  same  way  till  both  solutions  just  become  red. 
It  will  be  observed  that  whereas  about  i  c.c.  of  hydrochloric 
acid  brings  about  the  change  of  colour  (owing  to  its  relatively 
high  concentration  in  H-  ions),  several  c.c.  of  acetic  acid  are 
required  to  produce  the  same  effect,  owing  to  the  much  smaller 
H'  ion  concentration  of  the  latter  solution.  If  now  a  strong 
solution  of  sodium  acetate  is  added  to  the  last  solution,  the 
yellow  colour  of  the  methyl-orange  will  be  restored;  the 
acetate  reduces  the  strength  of  the  acid  to  such  an  extent 


3io       OUTLINES  OF  PHYSICAL  CHEMISTRY 

(p.  277)  that  the  H*  ion  concentration  is  no  longer  sufficient 
to  drive  back  the  ionisation  of  the  methyl -orange. 

The  effect  of  hydrolysis  may  be  illustrated  with  indicators  as 
follows :  Each  of  two  beakers  contains  50  c.c.  of  1/2  n  hydro- 
chloric acid  and  a  few  drops  of  methyl-orange  and  phenol- 
phthalein  respectively.  If  n  ammonium  hydroxide  is  slowly 
added  to  the  solution  containing  methyl-orange,  the  colour 
will  change  when  about  25  c.c.  of  ammonia  has  been  added, 
but  a  much  greater  quantity  of  the  same  solution  will  be  re- 
quired to  redden  the  phenolphthalein  solution.  The  explanation 
of  this  behaviour  has  already  been  given.  Owing  to  the  fact 
that  the  ammonium  salt  of  phenolphthalein  is  considerably 
hydrolysed,  it  is  necessary  to  add  a  fair  excess  of  the  base 
before  the  coloured  phenolphthalein  ions  are  produced  in 
considerable  amount. 

The  Solubility  Product — The  conception  of  the  solubility 
product  may  be  illustrated  by  the  method  employed  by  Nernst 
in  proving  the  formula  experimentally.  A  saturated  solution 
of  silver  acetate  is  prepared  by  shaking  the  finely-powdered 
salt  with  water  for  some  time.  To  a  few  c.c.  of  the  solution 
in  a  test-tube  a  few  c.c.  of  a  fairly  concentrated  solution  of 
silver  nitrate  are  added,  and  to  another  portion  of  the  acetate 
solution  a  solution  of  sodium  acetate  equivalent  in  strength 
to  the  silver  nitrate  solution,  and  the  mixtures  are  well  shaken. 
In  each  tube  a  precipitate  of  silver  acetate  will  be  formed. 

Complex  Ions — The  evidence  in  favour  of  the  view  that  in 
solutions  of  silver  salts  in  potassium  cyanide  the  silver  is 
mainly  present  as  a  constituent  of  a  complex  anion,  Ag(CN)'2, 
is  that  the  silver  migrates  towards  the  anode  during  electrolysis. 
The  copper  in  Fehling's  solution  is  also  mainly  present  as  a 
component  of  a  complex  anion,  as  may  readily  be  shown 
qualitatively  by  a  simple  experiment  described  by  Kiister.  A 
U-tube  is  about  half-filled  with  a  dilute  solution  of  copper 
sulphate,  and  the  two  limbs  are  then  nearly  filled  up  with  a 
dilute  solution  of  sodium  sulphate  in  such  a  way  that  the 


EQUILIBRIUM  IN  ELECTROLYTES  311 

boundaries  remain  sharp.  A  second  U-tube  is  filled  in  an 
exactly  similar  way  with  Fehling's  solution  in  the  lower  part 
and  an  alkaline  solution  of  sodium  tartrate  in  the  upper  part, 
the  arrangement  being  such  that  the  Fehling's  solution  in  the 
one  tube  stands  at  the  same  level  as  the  copper  sulphate  solu- 
tion in  the  other  tube.  The  U-tubes  are  then  connected  by  a 
bent  glass  tube,  filled  with  sodium  sulphate  solution,  and  with  the 
ends  dipping  in  the  sulphate  and  tartrate  solutions  respectively. 
A  small  current  is  then  sent  through  the  U-tubes  in  series,  by 
means  of  poles  dipping  in  the  outer  limbs  of  the  tubes, 
and  after  a  time  it  will  be  observed  that  the  copper  sulphate 
boundary  has  moved  with  the  positive  current,  whilst  the 
coloured  boundary  in  the  other  tube  has  moved  against  the 
positive  current  towards  the  anode.  It  is  therefore  evident 
that  in  the  latter  case  the  copper  is  present  in  the  anion,  as 
stated  above. 

Chemical  Activity  and  lonisation — The  great  difference  in 
chemical  and  electrical  activity  produced  by  ionisation  is  well 
shown  by  comparing  the  properties  of  solutions  of  hydrochloric 
acid  gas  in  water  and  in  an  organic  solvent  such  as  toluene. 
Whilst  the  former  solution  conducts  the  electric  current  and 
dissolves  calcium  carbonate  rapidly,  the  latter  solution  is  a 
non-conductor,  and  has  little  or  no  effect  on  calcium  carbon- 
ate. 

The  same  fact  is  illustrated  by  the  interaction  of  silver  nitrate 
with  potassium  bromide,  ethyl  bromide  and  phenyl  bromide 
respectively  in  alcoholic  solution.  Approximately  5  per  cent, 
solutions  of  the  bromides  in  ethyl  alcohol  are  prepared,  and 
to  each  solution  is  added  a  few  c.c.  of  a  saturated  solution  of 
silver  nitrate  in  alcohol.  With  the  potassium  bromide  there  is 
an  immediate  precipitate,  the  action  being  ionic.  With  ethyl 
bromide  the  reaction  is  very  slow,  and  there  is  no  apparent 
reaction  with  phenyl  bromide.  The  reaction  between  silver 
nitrate  and  ethyl  bromide  is  a  good  example  of  a  chemical  change 


3i2       OUTLINES  OF  PHYSICAL  CHEMISTRY 

which  is  not  ionic,  as  far  as  one  of  the  reacting  substances  (the 
ethyl  bromide)  is  concerned. 

Non -ionic  chemical  changes  may,  however,  be  very  rapid. 
A  solution  of  copper  oleate  in  perfectly  dry  benzene  reacts 
immediately  with  a  solution  of  hydrochloric  acid  gas  in  dry 
benzene,  with  precipitation  of  cupric  chloride  (Kahlenberg). 


CHAPTER  XII 
COLLOIDAL  SOLUTIONS.1     ADSORPTION 

Colloidal  Solutions.  General — Up  to  the  present  we 
have  dealt  with  substances  which  on  the  basis  of  their  osmotic 
and  electrical  behaviour  may  be  classed  either  as  electrolytes 
or  non -electrolytes.  In  the  present  chapter  we  are  concerned 
with  a  new  type  of  substance  which  differs  in  many  respects 
both  from  typical  electrolytes  and  non -electrolytes.  The  first 
discoveries  in  this  field  we  owe  to  Thomas  Graham  (1861)  who 
found  that  whilst  certain  substances  diffuse  rapidly  in  solution 
and  readily  pass  through  animal  and  vegetable  membranes, 
other  substances  diffuse  very  slowly  in  solution  and  are  unable 
to  pass  through  membranes.  To  the  first  class  of  substances, 
which  can  readily  be  obtained  in  crystalline  form,  Graham  gave 
the  name  crystalloids,  whilst  the  members  of  the  other  class, 
which  cannot  as  a  rule  be  obtained  in  crystalline  form,  were 
termed  colloids.  Most  inorganic  acids,  bases  and  salts  and 
many  organic  compounds,  such  as  acetic  acid,  cane  sugar  and 
urea  are  crystalloids;  starch,  gum,  gelatine,  caramel  and  pro- 
teins in  general  belong  to  the  group  of  colloids.  The  dif- 
ferences in  the  rates  of  diffusion  in  aqueous  solution  of  typical 
crystalloids  and  colloids  are  illustrated  in  the  following  numbers, 
valid  for  i  o°,  which  represent  the  relative  times  required  for  the 
same  amount  of  diffusion  of  different  substances. 

1  For  fuller  details  of  the  subjects  treated  of  in  this  chapter  see  Philip, 
Physical  Chemistry  :  Its  Bearing  on  Biology  and  Medicine  (Arnold,  19 10) ; 
Freundlich,  Kapillarchetnie  (Leipzig,  1909) ;  Wolfgang  Ostwald,  Kolloid- 
chemie  (Dresden,  191 1). 

313 


314      OUTLINES  OF  PHYSICAL  CHEMISTRY 


Crystalloids. 

f 

Colloids. 

Substance 
Relative  times  of 
equal  diffusion    . 

HC1 

i 

NaCl 
2-3 

Cane  Sugar 
7 

Albumen 
49 

Caramel 
98 

As  under  equivalent  conditions  the  rate  of  diffusion  is  pro- 
portional to  the  osmotic  pressure  of  the  solute,  it  follows  that  the 
osmotic  pressure  of  dissolved  colloids  is  very  small  and  therefore 
that  their  molecular  weights  are  very  high.  This  view  as  to  the 
high  molecular  weight  of  colloids  was  held  by  Graham,  who 
suggested  that  the  differences  in  behaviour  of  the  two  classes 
of  substance  might  be  connected  with  the  much  greater  size 
of  colloidal  particles  as  compared  with  dissolved  particles  of 
crystalloids.  It  may  be  said  at  once  that  later  investigation  has 
fully  confirmed  the  view  as  to  the  high  molecular  weight  of 
colloids  in  solution. 

As  was  to  be  anticipated,  the  later  developments  of  the 
subject  have  led  to  modifications  of  Graham's  views  in  some 
essential  respects.  In  the  first  place  it  has  been  shown  that 
colloids  are  not  a  special  class  of  substances  ;  the  colloidal 
state  is  a  condition  into  which  practically  all  chemical  substances 
can  be  brought  by  suitable  methods.  For  example,  metals  such 
as  silver  and  platinum,  and  even  salts  such  as  silver  chloride 
and  sodium  chloride,  all  of  which  are  ordinarily  met  with  in 
crystalline  form,  can  be  obtained  in  colloidal  solution.  There 
are,  however,  great  differences  in  the  readiness  with  which  dif- 
ferent substances  can  be  brought  into  the  colloidal  state,  and 
some  substances,  such  as  starch  and  gelatine,  are  only  met 
with  in  solution  in  the  colloidal  form. 

A  further  point,  which  has  been  established  within  the  last 
few  years,  is  that  colloidal  solutions  are  not  solutions  in  the 
ordinary  sense  of  the  term.  A  true  solution  has  been  defined 
as  a  homogeneous  mixture,  and  therefore  consists  of  a  single 


COLLOIDAL  SOLUTIONS.     ADSORPTION        315 

phase.  A  colloidal  solution,  on  the  other  hand,  such  as  col- 
loidal platinum,  can  be  shown  to  be  heterogeneous ;  that  is,  it 
consists  of  two  phases  at  least.  As  we  shall  see  later,  however, 
all  intermediate  stages  exist  between  colloidal  solutions  and 
true  solutions  on  the  one  hand,  and  between  colloidal  solutions 
and  ordinary  suspensions  on  the  other.  Within  the  last  few 
years  it  has  become  usual  to  speak  of  the  phase  present  in 
separate  particles  as  the  disperse  phase  and  the  liquid  in  which 
it  is  distributed  as  the  dispersion  medium. 

The  preparation  of  some  typical  colloidal  solutions,  and 
the  properties  characteristic  of  the  colloidal  state,  will  now  be 
considered. 

Preparation  of  Colloidal  Solutions — A  suitable  colloidal 
solution  for  demonstration  purposes  is  that  of  arsenious  sul- 
phide. It  is  prepared  by  passing  hydrogen  sulphide  through  a 
cold  aqueous  solution  of  arsenious  oxide,  free  from  electrolytes, 
sufficiently  long  to  ensure  conversion  to  arsenious  sulphide. 
Excess  of  hydrogen  sulphide  is  then  removed  as  far  as  possible 
by  a  stream  of  hydrogen.  The  resulting  solution,  after  filtra- 
tion, is  yellowish  in  colour  and  clear  by  transmitted  light,  but 
appears  turbid  by  reflected  light.  The  degree  of  dispersion  of 
the  sulphide  (that  is,  the  size  of  the  particles)  varies  greatly 
with  the  mode  of  preparing  the  solution. 

Silicic  acid  is  obtained  in  colloidal  solution  by  slowly  add- 
ing a  solution  of  sodium  silicate  to  excess  of  hydrochloric  acid 
and  then  removing  the  sodium  chloride  and  free  hydrochloric 
acid  by  dialysis.  The  simplest  form  of  dialyser  is  a  tube  of 
parchment  paper  into  which  the  mixture  is  poured.  The  tube 
is  then  suspended  by  its  ends  in  water  which  is  continually  re- 
newed, and  in  course  of  time  the  crystalloids  are  completely 
removed  by  diffusion  through  the  membrane,  leaving  a  pure 
colloidal  solution  of  silicic  acid. 

Ferric  hydroxide  is  obtained  in  colloidal  solution  (so  called 
"  dialysed  iron  ")  by  dissolving  the  freshly  precipitated  hydrox- 
ide in  a  dilute  solution  of  ferric  chloride,  and  removing  the 


316       OUTLINES  OF  PHYSICAL  CHEMISTRY 

ferric  chloride  by  dialysis.  Other  colloidal  hydroxides  may  be 
obtained  by  an  analogous  method. 

The  preparation  of  colloidal  platinum  according  to  Bredig 
has  already  been  described  (p.  232).  Other  colloidal  metals 
(e.g.  gold,  silver,  palladium)  have  been  prepared  by  the  same 
method.  Colloidal  gold  and  other  metals  can  also  be  pre- 
pared by  reducing  the  corresponding  salts  in  aqueous  solution. 

Gelatine,  gum  and  certain  other  substances  form  colloidal 
systems  on  simple  solution  in  water. 

Osmotic  Pressure  and  Molecular  Weight  of  Colloids — 
It  has  already  been  mentioned  that,  corresponding  with  their 
slow  rate  of  diffusion,  the  osmotic  pressure  of  colloidal  solutions 
is  very  small.  This  is  fully  confirmed  by  recent  investigations, 
but  direct  quantitative  measurements  by  different  observers 
have  not  led  to  very  concordant  results.  One  of  the  principal 
sources  of  error  has  been  the  difficulty  of  freeing  colloids  com- 
pletely from  electrolytes,  which  even  in  very  small  concentra- 
tion have  considerable  osmotic  pressure.  This  difficulty  is  to 
some  extent  overcome  by  using  another  colloid,  such  as  parch- 
ment paper,  as  semi-permeable  membrane  ;  one  colloid,  whilst 
usually  permeable  for  crystalloids,  is  impermeable  to  other  col- 
loids. Hence,  as  parchment  paper  and  other  membranes  are 
permeable  for  dissolved  salts,  the  latter  cannot  set  up  a  lasting 
osmotic  pressure,  and  a  pressure  which  persists  for  a  consider- 
able time  may  be  regarded  as  due  to  the  colloid  only. 

As  illustrating  the  nature  of  the  results  obtained,  Lillie,1 
using  a  collodion  membrane,  found  that  a  solution  of  egg  albu- 
men containing  12-5  grams  per  litre  gave  an  osmotic  pressure 
of  20  mm.  of  mercury  at  room  temperature.  According  to 
Waymouth  Reid  the  osmotic  pressure  of  a  i  per  cent,  solution 
of  haemoglobin  is  about  4  mm.  of  mercury,  but  much  higher 
values,  indicating  a  molecular  weight  of  about  16,000,  were  ob- 
tained by  Roaf  (1910). 

1Amer.  Journal  of  Physiology,  1907,  20,  127. 


COLLOIDAL  SOLUTIONS.     ADSORPTION        317 

Moore  and  Roaf l  observed  a  pressure  of  about  70  mm.  of 
mercury  for  a  10  per  cent,  solution  of  gelatine,  which  remained 
fairly  steady  for  two  months. 

The  effect  of  electrolytes  on  the  magnitude  of  the  osmotic 
pressure  depends  on  the  nature  of  the  colloid.  Neutral  salts 
in  many  cases  lower  the  osmotic  pressure  of  colloids,  a  result 
probably  due  to  partial  coagulation  of  the  colloidal  particles. 
Acids  and  bases  often  raise  the  osmotic  pressure  of  colloids, 
probably  in  consequence  of  chemical  combination. 

As  the  osmotic  pressure  of  colloids  is  so  small  when  measured 
by  the  direct  method  it  will  readily  be  understood  that  the 
freezing  points  and  boiling  points  of  colloidal  solutions  scarcely 
differ  from  those  of  pure  water.  This  is  evident  when  we 
consider  that  a  solution  of  osmotic  pressure  70  mms.  (as 
observed  in  the  experiments  just  described)  would  have  a 
freezing-point  less  than  yj^0  below  that  of  water. 

Optical  Properties  of  Colloidal  Solutions — The  majority 
of  colloidal  solutions  appear  homogeneous  even  under  the 
highest  power  of  the  microscope,  but  their  heterogeneous  char- 
acter is  established  by  means  of  the  so-called  "Tyndall  phe- 
nomenon ".  When  a  ray  of  light  enters  a  darkened  room  its 
path  is  recognised  by  the  scattering  of  the  light  at  the  surface 
of  dust  particles.  Similarly,  the  path  of  a  beam  passed  through 
a  colloidal  solution  can  be  detected  by  the  scattering  of  the 
light  at  the  surface  of  the  ultramicroscopic  particles,  whereas 
no  indication  is  afforded  of  the  path  of  a  beam  passed  through 
a  solution  which  contains  no  particles  exceeding  a  certain 
magnitude.  Light  which  has  passed  through  a  colloidal  solu- 
tion is  partially  or  completely  polarised. 

The  Tyndall  phenomenon  has  recently  been  utilised  in  the 
construction  of  the  ultramicroscope,  by  means  of  which  our 
knowledge  of  colloidal  solutions  has  been  greatly  extended. 
An  intense  beam  of  light  (the  arc  light  or,  better,  sunlight)  is 

1  Moore  and  Roaf,  Biochem.  Jonm.  1906,  2,  34. 


3i8       OUTLINES  OF  PHYSICAL  CHEMISTRY 

directed  on  a  very  thin  layer  of  the  colloid  and  the  latter 
examined  by  a  microscope  at  right  angles  to  the  direction  of 
the  beam,  the  entrance  of  light  from  other  sources  being  pre- 
vented. When  a  homogeneous  liquid  is  used  the  field  remains 
quite  dark,  but  when  the  liquid  contains  discrete  particles  their 
presence  is  indicated  by  the  appearance  of  colourless  or  (for 
smaller  particles)  characteristically  coloured  luminous  moving 
points  on  a  dark  background.  It  must  be  emphasised  that 
the  ultramicroscope  does  not  render  the  particles  themselves 
visible,  but  only  shows  the  light  reflected  from  them,  so  that 
such  observations  afford  no  information  as  to  the  shape,  colour, 
etc.,  of  the  particles. 

The  average  size  of  the  particles  in  a  colloidal  solution  can 
be  estimated  indirectly  by  counting  the  number  in  a  given 
volume  and  determining  the  total  amount  of  substance  by 
analysis.  In  this  way  it  has  been  shown  that  the  particles  vary 
greatly  in  magnitude,  depending  on  the  nature  and  mode  of 
preparation  of  the  colloidal  solution,  from  such  as  are  visible  in 
the  ordinary  microscope  to  those  not  resolvable  even  by  the 
ultramicroscope.  Particles  visible  in  the  ordinary  microscope 
(diameter  exceeding  250  /x/x,  where  /x  =  crooi  mm.  and  /x/x  = 
o  "ooooo i  mm.)  are  termed  by  Zsigmondy  microns,  those  detected 
only  by  the  ultramicroscope  (diameter  6-250  /x/x.)  are  termed 
submicrons,  and  those  of  diameter  less  than  6  /x/x  amicrons. 

For  comparative  purposes  it  may  be  mentioned  that  the  wave- 
length of  sodium  light  is  589  /x/x.  It  has  been  calculated l  that 
the  diameter  of  an  ether  molecule  is  about  0*6  x  io~6  mm. 
=  0-6  /x/x,  so  that  the  smallest  particle  which  can  be  detected 
by  the  ultramicroscope  has  a  diameter  only  ten  times  greater 
than  that  of  an  average  chemical  molecule. 

Brownian  Movement — When  a  colloidal  solution  contain- 
ing microns  (e.g.  mercuric  sulphide,  suspension  of  gum  mastic) 
is  examined  under  the  microscope,  the  particles  are  seen  to  be 

1  Perrin,  loc.  cit.,  p.  50. 


COLLOIDAL  SOLUTIONS.     ADSORPTION        319 

performing  continuous  irregular  movements  (R.  Brown,  1827) 
"  They  go  and  come,  stop,  start  again,  mount,  descend,  remount 
again,  without  in  the  least  tending  towards  immobility  "  (Perrin). 
Observations  with  the  ultra- microscope  show  that  the  move- 
ments are  the  more  brisk  the  smaller  the  particles  and  the  less 
the  viscosity  of  the  liquid,  and  they  become  more  rapid  with 
rise  of  temperature.  The  phenomenon  persists  for  years ;  it  is 
not  due  to  any  external  cause,  such  as  alterations  of  temperature 
or  of  illumination,  and  it  is  now  generally  agreed  that  it  is  a 
consequence  of  "the  incessant  movements  of  the  molecules  of 
the  liquid  which,  striking  unceasingly  the  observed  particles, 
drive  them  about  irregularly  through  the  fluid,  except  in  the 
case  where  these  impacts  exactly  counterbalance  one  another  " 
(Perrin,  loc.  tit.}.  It  has  been  shown  within  the  last  few  years, 
more  particularly  by  Perrin,  that  the  rates  of  movement  of  the 
particles  are  in  entire  accord  with  those  deducted  on  the  basis 
of  the  molecular-kinetic  theory,  which  amounts  to  an  experi- 
mental proof  of  the  atomic  constitution  of  matter  and  of  the 
kinetic  nature  of  heat *  (cf.  p.  32). 

Electrical  Properties  of  Colloids — When  two  plates  are 
placed  at  some  distance  apart  in  a  colloidal  solution  and  con- 
nected with  a  source  of  E.M.F.  it  will  be  found  as  a  rule  that  the 
particles  move  slowly  towards  the  anode  or  cathode ;  in  other 
words,  they  behave  as  if  they  are  electrically  charged.  The 
simplest  method  of  making  the  experiment  is  to  place  the 
colloidal  solution  in  the  lower  part  of  a  U-tube,  which  is  filled 
up  on  both  sides  with  distilled  water  in  which  the  electrodes 
are  placed.  The  latter  are  then  connected  with  the  terminals 
of  the  lighting  circuit  (100-200  volts)  and  the  speed  of  the 
moving  boundary  observed  directly.  The  results  show  that 
particles  of  all  kinds  move  at  the  rate  of  10-40  x  io~5.  cm 
per  second  for  a  potential  gradient  of  i  volt  per  cm.  As  we  have 
seen,  this  is  also  the  order  of  the  migration  velocity  of  the  ions 

'Ostwald,  Grundriss  der  Allg.  Chemie.,  p.  iv,  545. 


320       OUTLINES  OF  PHYSICAL  CHEMISTRY 

(p.  253)  and  we  have  therefore  the  remarkable  fact  that  particles 
of  all  sizes — microns,  submicrons,  amicrons,  ions — move  with 
approximately  the  same  speed  in  the  electric  field. 

In  the  case  of  the  noble  metals  (gold,  platinum,  silver,  etc.)  and 
the  sulphides  (arsenic  and  antimony  trisulphides)  the  particles 
are  negatively  charged  and  move  towards  the  anode,  whilst 
hydroxides  (ferric  and  aluminium  hydroxides,  etc.)  and  haemo- 
globin are  positively  charged.  The  charge  on  some  colloids 
can,  however,  be  altered  in  sign  by  certain  additions  to  the 
medium.  Thus  Hardy  has  shown  that  when  acid  is  added  to 
egg  albumen  it  migrates  to  the  cathode,  whilst  in  alkaline  solu- 
tion it  moves  towards  the  anode.  The  condition  in  which  the 
colloid  is  uncharged  is  known  as  the  isoelectric  point,  which  in 
the  case  of  egg  albumen  occurs  in  approximately  neutral  solu- 
tion. 

Precipitation  of  Colloids  by  Electrolytes— It  is  a  re- 
markable fact  that  many  colloidal  solutions  are  readily  coagu- 
lated by  the  addition  of  electrolytes.  When,  for  example,  a 
few  drops  of  barium  chloride  solution  are  added  to  a  colloidal 
solution  of  arsenic  sulphide  the  solution  becomes  turbid,  and  in 
a  few  minutes  the  sulphide  has  completely  separated  in  flocks. 
The  process  can  be  followed  under  the  ultramicroscope,  and 
is  seen  to  consist  in  a  gradual  aggregation  of  the  particles 
(amicrons  to  submicrons,  then  to  microns  and  finally  to  large 
flocks)  the  Brownian  movement  becoming  slower  and  slower 
and  finally  ceasing. 

The  efficiency  of  different  electrolytes  in  the  coagulation  of 
arsenic  sulphide  depends  mainly  on  the  valency  of  the  anion 
and  is  largely  independent  of  its  nature.  The  molar  concen- 
trations of  A1C13,  BaCl2,  and  KC1  required  to  produce  same 
degree  of  coagulation  under  conditions  otherwise  equivalent 
areas  follows:  i:  7-4:  532  (Freundlich).  With  solutions  of 
ferric  hydroxide,  on  the  other  hand,  the  coagulating  power  of 
electrolytes  is  practically  independent  of  the  valency  of  the 
cation,  and  is  determined  chiefly  by  the  valency  of  the  anion. 


COLLOIDAL  SOLUTIONS.     ADSORPTION        321 

Thus  the  molar  concentrations  of  K2SO4  and  KC1  which  pro- 
duced the  same  effect  are  in  the  ratio  i  :  45. 

When  it  is  remembered  that  the  particles  of  arsenious  sul- 
phide are  negatively  charged  and  those  of  ferric  hydroxide 
positively  charged  the  bearing  of  these  results  at  once  becomes 
evident.  The  ion  which  brings  about  the  coagulation  of  a 
colloidal  solution  is  the  one  carrying  a  charge  of  opposite  sign  to 
that  on  the  colloidal  particles  (Hardy).  Further  investigation 
has  shown  that  this  rule  can  be  extended  to  the  reciprocal 
action  of  colloidal  particles,  inasmuch  as  two  colloidal  solu- 
tions containing  particles  of  contrary  sign  coagulate  on  mixing 
(e.g.  colloidal  platinum  and  ferric  hydroxide)  whilst  colloids 
of  the  same  sign  are  practically  without  influence  on  each 
other. 

As  regards  the  nature  of  the  coagulation,  it  has  been  shown 
that  in  certain  cases  at  least  the  electrolyte  is  partially  decom- 
posed, the  precipitating  ion  being  carried  down  along  with  the 
precipitate  and  the  inactive  ion  left  in  solution  in  combination 
with  another  ion.  In  order  to  understand  this  phenomenon  it 
is  necessary  to  consider  rather  more  fully  the  question  of  the 
stability  of  a  colloidal  solution.  It  has  been  shown  by  Hardy, 
Burton  and  others  that  certain  colloids  reach  their  point  of  maxi- 
mum instability  (that  is,  coagulate  most  readily)  when  the 
charge  on  the  particles  (as  indicated  by  their  behaviour 
under  the  influence  of  a  potential  gradient)  reaches  a  minimum. 
Taking  as  illustration  the  coagulation  of  arsenious  sulphide  by 
potassium  chloride  solution  we  may  assume  that  some  of  the 
salt  is  taken  up  by  the  colloidal  particles,  the  negative  charges 
on  the  latter  are  neutralized  by  the  K-  ions,  with  the  result  that 
the  particles  become  unstable,  aggregate  and  fall  out  of  solution 
carrying  the  K-  ions  along  with  them  (presumably  as  a  salt). 
The  Cl-  ions  are  left  in  the  solution  along  with  an  equivalent 
of  H-  ions  derived  from  the  hydrogen  sulphide  always  associated 
with  the  colloidal  sulphide.  This  is  the  so-called  "adsorp- 
tion "  theory  of  coagulation.  Other  theories  of  the  pheno- 


322        OUTLINES  OF  PHYSICAL  CHEMISTRY 

menon,    notably    Billiters   "condensation"   theory,   have  also 
been  proposed,  but  cannot  be  dealt  with  here.1 

Suspensions,  Suspensoids  and  Emulsoids — All  the  pro- 
perties discussed  in  the  previous  sections  (with  the  possible 
exception  of  the  action  of  electrolytes  on  the  stability)  are 
characteristic  of  colloidal  solutions  in  general,  as  well  as  of 
suspensions  of  particles  easily  visible  under  the  microscope. 
As  typical  '•  suspensions  "  may  be  mentioned  clay,  finely  divided 
charcoal  or  gum  mastic  stirred  up  with  water.  They  consist 
of  a  practically  insoluble  solid  phase,  distributed  in  a  liquid, 
usually  water.  The  particles  settle  to  the  bottom  of  the  vessel 
more  or  less  rapidly,  depending  on  their  magnitude,  but  the 
system  "  clears  "  much  more  rapidly  when  electrolytes  are  added 
(cf.  previous  section).  From  the  suspensions  we  pass  through 
a  series  of  intermediate  stages  to  the  suspensoids  or  suspension 
colloids,  the  heterogeneous  character  of  which  is  only  recognised 
by  Tyndall's  phenomenon  or  by  the  ultramicroscope.  Like 
the  suspensions,  they  consist  of  a  solid  phase  distributed  in  a 
liquid,  generally  water.  "  Colloidal  solutions  "  are  divided  into 
two  fairly  well-defined  classes,  the  suspension  colloids  or  sus- 
pensoids just  mentioned  and  the  emulsion  colloids  or  emulsoids. 
The  suspensoids  are  scarcely  more  viscous  than  water,  do  not 
gelatinise  and  are  readily  precipitated  by  electrolytes.  The 
emulsoids  are  viscous,  become  gelatinous  under  certain  condi- 
tions and  are  not  readily  precipitated  by  electrolytes.  The 
colloidal  metals,  sulphides  and  hydroxides  are  suspensoids; 
silicic  acid,  gelatine,  gum,  mucilage  of  starch  and  proteins  in 
general  are  emulsoids.  To  these  experimental  differences  be- 
tween the  two  classes  it  may  be  added  that  the  dispersed  sub- 
stance in  an  emulsoid  is  probably  present  partly  as  a  liquid  or 
semi-liquid  phase  and  partly  in  true  solution.  From  this  point 
of  view  an  emulsoid  such  as  an  aqueous  solution  of  gelatine  is 
made  up  of  two  phases,  one  rich  in  water  and  containing  a 

1  Wo.  OstwaW,  Kolioidchemic,  p.  499. 


COLLOIDAL  SOLUTIONS.     ADSORPTION        323 

little  gelatine  in  true  solution,  the  other  rich  in  gelatine,  but 
containing  a  little  water  (Hardy). 

It  is  a  familiar  fact  that  an  emulsoid  such  as  silicic  acid  can 
be  obtained  as  a  clear,  apparently  homogeneous  solution 
(p.  315)  which  on  long  standing,  more  rapidly  on  boiling  or  on 
treatment  with  electrolytes,  changes  to  a  semi-solid  amorphous 
mass.  The  clear  solution  is  termed  a  sol,  the  gelatinous  mass 
a  gel.  The-  term  sol  is  also  applied  to  suspensoids.  When  the 
electrolyte  is  removed  by  washing  and  the  gel  is  again  treated 
with  water  certain  emulsoids,  such  as  the  proteins,  return  to  the 
sol  modification  (more  readily  on  warming)  and  are  therefore 
termed  reversible  colloids.  Suspensoids  in  general  and  certain 
emulsoids,  such  as  silicic  acid,  do  not  return  to  the  soluble 
form  under  these  conditions  and  are  therefore  known  as  irre- 
versible colloids. 

The  coagulation  of  emulsoids  by  electrolytes  seems  to  be 
entirely  different  to  the  action  on  suspensoids,  but  is  by  no 
means  well  understood.  Whether  the  electrical  character  of 
the  particles  and  of  the  electrolyte  plays  any  part  in  the  process 
is  doubtful ;  in  fact  silicic  acid  sol  seems  to  be  most  stable  in 
the  electrically  neutral  condition.  The  addition  of  neutral 
salts  in  considerable  concentration  causes  the  separation  of  the 
solid  phase,  but  the  ratio  of  the  activities  of  different  electrolytes 
is  quite  different  from  that  observed  for  suspension  colloids 
and  resembles  the  "salting  out"  observed,  for  instance,  in  the 
effect  on  the  solubility  of  gases  in  water  (p.  84). 

Filtration  of  Colloidal  Solutions — It  has  already  been 
pointed  out  that  systems  of  all  degrees  of  dispersion  are  met 
with,  from  those  containing  large  particles  easily  visible  under 
the  microscope  to  molecular  dispersed  systems,  which  we  term 
true  solutions.  It  is  evident,  however,  that  true  solutions  are 
only  apparently  homogenous  ;  the  solute  particles  are  so  minute 
as  to  escape  our  present  methods  of  detecting  heterogeneity. 
As  already  explained,  the  size  of  colloidal  particles  can  be 
roughly  estimated  by  counting  the  number  in  a  given  volume 


324        OUTLINES  OF  PHYSICAL  CHEMISTRY 

of  solution  containing  a  known  weight  of  the  disperse  phase. 
Another  method  which  has  recently  come  into  use  for  this  pur- 
pose is  to  use  filters  with  pores  of  different  sizes.  Bechhold,1 
who  has  done  much  work  on  this  subject,  uses  filter-papers 
impregnated  with  gelatine  solutions  of  different  concentrations, 
and  finds  that  a  filter  with  2  per  cent  of  gelatine  retains  all 
particles  of  diameter  less  than  44ynfi,  one  containing  4-4*5  per 
cent,  is  required  to  retain  the  much  smaller  particles  of  serum - 
albumen,  the  average  molecular  weight  of  which  is  about  10,000 
(3,000-15,000).  The  permeability  of  such  filters  is  of  course 
influenced  by  the  pressure  under  which  filtration  is  carried  out. 
A  very  early  form  of  the  "ultra-filter,"  introduced  by  Martin, 
consists  of  an  ordinary  porcelain  filter  impregnated  with  gela- 
tine. 

Adsorption.  General — It  is  a  familiar  fact  that  when 
water  containing  a  colouring  matter  such  as  caramel  or  litmus 
is  shaken  up  with  finely  divided  charcoal  the  latter  on  settling 
carries  down  the  colouring  matter  with  it,  leaving  the  water 
practically  colourless.  Further  investigation  shows  that  other 
substances,  including  electrolytes  and  non-electrolytes  as  well 
as  colloids,  are  largely  taken  up  by  charcoal  from  aqueous  solu- 
tion, and  that  other  finely  divided  substances  have  the  same 
property.  Charcoal  has  also  the  power  of  taking  up  gases,  es- 
pecially those  which  are  easily  liquefied,  such  as  ammonia  and 
sulphur  dioxide. 

The  nature  of  this  phenomenon  will  be  more  readily  under- 
stood in  the  light  of  some  quantitative  observations,  and  for 
this  purpose  the  results  of  a  series  of  experiments  carried  out 
by  Schmidt 2  on  the  taking  up  of  acetic  acid  from  aqueous 
solution  by  charcoal  are  quoted.  Animal  charcoal  (in  quan- 
tities of  5  grams)  was  shaken  up  with  aqueous  solutions  of  acetic 
acid  (100  ccs.  in  each  case)  of  different  concentrations  and  the 

1  Zcitsch.  Ghent.  Ind.  Kolloide,  1907,  2,  3. 

2  Zeitsch.  physikal  Chem,,  1910,  74,  689. 


COLLOIDAL  SOLUTIONS.     ADSORPTION         325 

amount  of  acid  remaining  in  the  water  phase  determined  by 
titration.  In  the  accompanying  table  Ac  represents  the  amount 
of  acetic  acid  taken  up  by  the  charcoal  and  Aw  the  amount  left 
in  solution  at  equilibrium. 

DISTRIBUTION     OF     ACETIC     ACID     BETWEEN     WATER     AND 
CHARCOAL. 

Ac  0*93  1*15  1*248         i -43  1-62 

Aw  0*0365          0*084         0*13          50*206         o'35o 

CC/GW    205    208    180   203    197 

As  the  volume  of  the  solution  and  the  amount  of  charcoal 
are  kept  constant,  the  amounts  given  in  the  table  are  propor- 
tional to  the  respective  concentrations,  Cc  and  Cw,  in  the  two 
phases.  The  figures  show  (i)  that  in  very  dilute  solution  the  acid 
is  almost  completely  taken  up  by  charcoal ;  (2)  that  the  con- 
centration in  the  charcoal  increases  much  less  rapidly  than  the 
concentration  in  the  aqueous  phase.  That  we  are  dealing  with 
true  equilibria  is  shown  by  the  fact  that  the  same  results  are 
obtained  from  either  side  (starting  from  concentrated  or  from 
dilute  solutions  of  the  acid). 

The  question  now  arises  as  to  how  these  observations  are  to 
be  interpreted.  In  the  first  instance  we  will  consider  whether 
the  process  is  a  physical  or  a  chemical  one,  and  if  the  former, 
whether  it  is  mainly  a  surface  condensation  or  whether  solid 
solutions  are  formed. 

It  appears  highly  improbable  for  several  reasons  that  the 
phenomena  are  chemical  in  nature.  In  the  first  place  the 
most  various  substances,  including  argon  and  the  other  in- 
active gases,  which  do  not,  as  far  as  is  known,  enter  into 
chemical  combination,  are  taken  up  by  charcoal.  Further,  a 
definite  chemical  compound  is  constant  in  composition  and, 
if  undissociated,  its  composition  is  independent  of  the  concentra- 
tion in  the  other  phase,  whereas,  as  the  table  shows,  the  composi- 
tion of  the  carbon-acetic  acid  system  varies  continuously 


326        OUTLINES  OF  PHYSICAL  CHEMISTRY 

within  wide  limits.  At  first  sight  it  would  appear  possible  to 
explain  the  results  as  being  due  to  the  formation  of  a  partially 
dissociated  solid  compound  in  equilibrium  with  its  products  of 
dissociation,  but  it  can  easily  be  shown  that  this  assumption  also 
is  incompatible  with  the  facts.  Applying  the  law  of  mass  action 
to  such  an  equilibrium  (in  the  liquid  phase]  we  have  (cf.  p.  173) 

[Absorbent]  wi  [Substance  taken  up]  w*/ [Compound]  "3  =  Const. 

where  the  square  brackets  represent  concentrations,  and  n\,  #2  and 
nz  represent  the  number  of  molecules  of  the  absorbent  (charcoal), 
the  substance  taken  up  (acetic  acid)  and  the  compound  re- 
spectively taking  part  in  the  equilibrium.  Further,  since  the 
active  masses  of  the  charcoal  and  the  compound  are  constant 

[Substance  taken  up]  =  Constant  (in  liquid  phase) 

that  is,  the  concentration  of  the  acetic  acid  in  the  solution 
must  be  constant  as  long  as  both  solid  phases  are  present. 
As  a  matter  of  fact,  the  concentration  of  acetic  acid  in  the 
solution  increases  continuously  with  the  total  concentration 
(compare  table),  so  that  no  second  solid  phase  (no  chemical 
compound)  can  be  present. 

The  formation  of  a  solid  dissociating  compound  from  a  solid 
phase  and  a  substance  in  solution  has  been  investigated  by 
Walker  and  Appleyard  in  the  case  of  diphenylamine  and  picric 
acid,  which  combine  to  form  the  slightly  soluble  brown  com- 
pound diphenylamine  picrate.1  Until  the  concentration  of 
the  acid  in  the  aqueous  layer  reached  ofo6  mols  per  litre  the 
solid  diphenylamine  (which  is  practically  insoluble  in  water) 
remained  colourless,  on  further  addition  of  picric  acid  the  brown 
diphenylamine  picrate  began  to  form,  and  finally  practically  all 
the  diphenylamine  was  converted  into  picrate,  the  concentration 
of  the  picric  acid  in  the  solution  remaining  all  the  time 
practically  constant  at  0*06  mols  per  litre.  It  is  evident  that 
1  Walker  and  Appleyard,  1896,  69,  1334. 


COLLOIDAL  SOLUTIONS.     ADSORPTION         327 

the  system  exactly  corresponds  with  the  calcium  carbonate — 
calcium  oxide — carbon  dioxide  equilibrium  already  considered 
(p.  1 74),  except  that  in  the  latter  case  the  substance  of  variable 
concentration  (the  carbon  dioxide)  is  in  a  gaseous  and  not  in 
a  liquid  phase. 

It  remains  to  consider  whether  the  phenomena  in 
question,  such  as  the  taking  up  of  acetic  acid  by  charcoal,  are 
due  to  surface  condensation  or  whether  solid  solutions  are 
formed.  It  would  seem  possible  to  decide  this  question  at 
once  by  observing  the  rate  of  establishment  of  equilibrium, 
since  surface  condensation  must  be  a  very  rapid  process,  and 
the  formation  of  a  solid  solution,  whereby  (in  the  case  under 
consideration)  one  substance  has  to  diffuse  into  the  interior  of 
the  other,  must  be  very  slow.  As  a  matter  of  fact  the  estab- 
lishment of  equilibrium  in  many  cases  (but  not  in  all  cases,  see 
below)  is  practically  instantaneous,  which  lends  strong  support 
to  the  surface  condensation  theory.  The  strongest  evidence  in 
favour  of  the  latter  theory,  however,  is  based  on  a  considera- 
tion of  the  ratio  of  the  distribution  of  the  substance  between 
the  two  phases.  It  has  been  shown  (p.  178)  that  when  a 
substance  distributes  itself  between  two  phases  the  ratio  of  the 
distribution  is  independent  of  the  concentration  provided  the 
molecular  weight  of  the  solute  is  the  same  in  both  solvents,  but 
if  the  molecular  weight  in  the  solvent  A  is  n  times  that  in  the 
solvent  B  then  \/CA/CB  is  constant,  which  may  be  written  more 
conveniently  thus:  C1A/X/CB=  Constant.  Now  the  table  on 
p.  325  shows  that  for  the  distribution  of  acetic  acid  between 
water  and  charcoal  the  formula  holds  approximately 

CC4/CW  =  Constant 

where  Cc  and  Cw  represent  the  concentrations  in  charcoal 
and  in  water  respectively.  Comparing  this  with  the  distri- 
bution formula,  Cj^/C,  =  Constant,  we  find  that 

i/x  =  4  or  x  =  1/4; 
that  is,  if  charcoal  and  water  may  be  regarded  as  two  solvents 


328        OUTLINES  OF  PHYSICAL  CHEMISTRY 

between  which  the  acetic  acid  is  distributed  then  the  molecular 
weight  of  the  acid  in  charcoal  is  1/4  that  in  water.  Now  it  was 
shown  by  Raoult  that  acetic  acid  exists  as  single  molecules 
in  aqueous  solution,  so  that  its  molecular  weight  in  charcoal, 
deduced  on  the  assumption  that  it  is  present  in  solid 
solution,  is  an  impossible  one.  Analogous  results  are  obtained 
with  other  solutes  and  other  absorbing  agents  and  it  follows  at 
once  that  the  "  solid  solution  "  explanation  of  the  phenomena 
under  consideration  is  definitely  disproved.  There  is  evidence, 
however,  that  in  some  cases  solid  solution  may  play  a  subsidi- 
ary part  in  the  phenomena.  Thus  Davis  1  found  that  when 
iodine  is  shaken  up  with  charcoal  a  very  rapid  action  is 
followed  by  a  slow  action,  the  latter  being  presumably  due 
to  the  slow  diffusion  of  the  iodine  into  the  interior  of  the 
charcoal.  Similarly  McBain 2  has  shown  that  when  hydrogen 
which  has  been  in  contact  with  charcoal  for  a  long  time  is 
pumped  out  the  greater  part  of  it  (that  condensed  on  the 
surface)  can  be  drawn  off  immediately,  but  a  small  residue 
(presumably  present  in  solid  solution)  can  only  be  removed 
very  slowly. 

It  has  now  been  established  that  the  phenomenon  under 
consideration  is  physical  in  nature  and  mainly  at  least  due  to 
surface  condensation.  In  order  to  distinguish  it  from  such 
a  process  as  the  absorption  of  gases  in  liquids,  an  example  of 
true  solution,  the  process  is  termed  Adsorptio?i,  and  the 
substance  which  is  condensed  on  the  surface  of  the  solid  phase 
is  said  to  be  adsorbed, 

Adsorption  of  Gases.  Adsorption  Formulae. — So  far 
we  have  been  concerned  mainly  with  the  adsorption  of  sub- 
stances from  solution.  It  is  now  necessary  to  deal  a  little  more 
in  detail  with  the  fact  already  mentioned,  that  porous  substances 
have  a  considerable  adsorptive  power  for  gases,  and  that  those 
gases  which  are  most  easily  liquefied  are  most  largely  adsorbed. 
The  nature  of  the  results  is  well  shown  by  the  recent  accurate 

1  Trans.  Chem.  Soc.,  1907,  91,  1666.         2  Phil.  Mag.,  1909,  18,  816. 


COLLOIDAL  SOLUTIONS.     ADSORPTION        329 

work  of  Homfray  l  and  of  Titoff 2  on  the  adsorption  of  gases  by 
charcoal.  The  amount  of  gas  adsorbed  is  proportional  to  the 
adsorbing  surface  and  is  the  greatei  the  lower  the  temperature 
and  the  higher  the  pressure.  Titoff  found  that  the  adsorption 
of  hydrogen  follows  Henry's  law,  so  that  the  formula 

CA/CB  =  Constant 

applies,  where  Cx  represents  the  concentration  in  the  solid 
phase,  CB  that  in  the  gas  phase.  The  other  gases  at  low  tem- 
peratures do  not  follow  Henry's  law,  but  the  results  are  repre- 
sented fairly  satisfactorily  by  a  formula  of  the  type  C^/A/CB  = 
Constant.  The  adsorptive  power  of  charcoal  for  traces  of  gas, 
especially  at  low  temperatures,  has  been  used  by  Dewar  to 
obtain  the  highest  vacua  yet  reached ;  the  pressures  were 
too  low  to  be  capable  of  measurement. 

It  has  been  shown  above  that  a  formula  of  the  type 
C^'*/CB  =  Constant — an  exponential  formula  —  affords  a 
fairly  satisfactory  representation  of  the  adsorption  both  of 
gases  and  dissolved  substances.  In  the  literature  it  is  met 
with  in  a  slightly  different  form,  which  will  now  be  given. 
Instead  of  writing  CA/;C/CB  we  may  put  CA/  CB  =  Constant. 
When  for  CA  we  put  x/m,  where  n  represents  the  amount  of  sub- 
stance adsorbed  by  m  grams  of  adsorbent,  we  obtain,  putting 
p  for  CB  and  i  /«  for  x,  the  formula 

x/m  =  fiplln 

where  ft  and  n  are  constant  at  constant  temperature.  When 
i/«  =  i  the  adsorption  follows  Henry's  law,  but  in  almost 
every  instance  i/«  is  considerably  less  than  i.  This  expresses 
the  important  fact  that  adsorption  is  relatively  greatest  from 
dilute  solution  and  falls  off  rapidly  with  the  concentration  (p.325). 

The  Cause  of  Adsorption — Adsorption  of  gases  and  liquids 
occurs  more  or  less  at  all  solid  surfaces,  a  well-known  case  in 
point  being  the  adsorption  of  moisture  by  glass  surfaces,  but 

1  Proc.  Roy  Soc.t  1910,  84,  A,  99. 

z  Zeitsch.  physikal  Chem.,  1910,  74,  641. 


330      OUTLINES  OF  PHYSICAL  CHEMISTRY 

it  is  only  when  the  surface  is  very  large  in  comparison  with  the 
weight  of  the  solid — as  in  the  case  of  porous  and  finely  divided 
substances — that  it  can  readily  be  measured.  We  have  now  to 
consider  why  the  concentration  in  the  surface  layers  differs  in 
many  cases  so  greatly  from  that  in  the  main  bulk  of  the 
liquid  or  gas  phase.  It  seems  probable  at  the  outset  that  this 
must  be  connected  with  molecular  attraction  at  the  boundary 
of  the  phases,  in  other  words  with  the  surface  tension  (p.  129) 
and  the  connection  between  surface  tension  and  adsorption  has 
been  deduced  theoretically  by  Willard  Gibbs  and  by  J.  J. 
Thomson.  From  the  general  standpoint  we  must  assume  that 
not  only  increased  concentration,  but  in  certain  systems  a 
lowering  of  concentration  at  the  surface,  as  compared  with  that 
in  the  main  bulk  of  liquid,  may  occur.  Calling  an  increase  of 
concentration  positive  adsorption  and  a  diminution  negative 
adsorption,  the  lule  may  be  expressed  as  follows : l  A  dissolved 
substance  is  positively  adsorbed  when  it  lowers  the  surface  tension, 
negatively  adsorbed  ivhen  it  raises  the  surface  tension.  The  first 
case  is  met  with  in  most  solutions  of  organic  compounds ;  the 
second  in  solutions  of  highly  ionised  inorganic  salts. 

Further  Illustrations  of  Adsorption — One  very  impor- 
tant process  in  which  adsorption  plays  a  prominent  part  is  the 
dyeing  of  fibres  such  as  wool  and  silk.  Whether  dyeing  is 
purely  an  adsorption  phenomenon  or  whether  chemical  action 
also  plays  a  part  has  given  rise  to  a  great  deal  of  discussion,  and 
is  by  no  means  finally  settled.  It  has  recently  been  shown 
that  the  distribution  of  crystal  violet,  new  magenta  and  patent 
blue  between  wool,  silk  and  cotton  on  the  one  hand  and  water 
on  the  other  is  satisfactorily  represented  by  the  adsorption 
formula,  and  the  value  of  the  exponent  */»  is  approximately 
the  same  as  when  charcoal  is  used  as  absorbent,  a  result  which 
supports  the  adsorption  theory.  On  the  other  hand,  Knecht 
showed  some  years  ago  that  when  the  basic  dye  crystal  violet 

1  C/.  Freundlich,  Kapillarchemie.,  p.  52. 


COLLOIDAL  SOLUTIONS.     ADSORPTION        331 

(the  hydrochloride  of  an  organic  base)  is  shaken  up  with  wool 
or  silk  the  dye  is  decomposed,  the  cation  combining  with  the 
fibre  and  the  anion  (in  this  case  Cl')  remaining  in  the  solution. 
This  result  was  first  described  as  a  case  of  double  decomposi- 
tion between  the  dye  and  the  fibre,  the  dye  combining  with  an 
organic  acid  in  the  fibre  to  form  a  salt,  and  ammonia  originally 
associated  with  the  fibre  combining  with  the  chlorine  to  form 
ammonium  chloride.  Freundlich  and  Neumann  l  have  shown, 
however,  that  in  certain  cases  at  least  the  chlorine  is  not  left 
in  the  solution  as  a  salt,  but  in  the  form  of  hydrochloric  acid. 
The  exact  form  in  which  the  adsorbed  dye  occurs  on  the  adsorb- 
ent does  not  seem  to  have  been  properly  established — the 
colour  appears  to  indicate  that  it  is  present  as  a  salt  and  not 
as  the  free  base. 

The  process  just  described  would  at  first  sight  appear  to  be 
an  ordinary  chemical  change,  but  further  investigation  shows 
that  charcoal  and  even  glass  pellets  split  up  dyes  in  an  exactly 
analogous  way,  the  cation  being  adsorbed  and  the  anion  re- 
maining in  solution.  It  can  scarcely  be  supposed  that  the 
charcoal  or  the  glass  enter  into  chemical  action  with  the  dyes. 
Phenomena  of  an  exactly  similar  nature  have  already  been  met 
with  in  connection  with  the  precipitation  of  colloids  by  electro- 
lytes (p.  319),  and  it  has  been  shown  that  they  are  connected 
with  the  electrical  character  of  the  colloidal  particles,  that  ion 
being  most  largely  adsorbed  which  carries  a  charge  of  opposite 
sign  to  that  on  the  colloid.  The  splitting  of  basic  dyes  de- 
scribed in  the  present  section  might  be  accounted  for  on  similar 
lines,  as  also  the  well-known  fact  that  an  "acid"  fibre  adsorbs 
more  particularly  basic  dyes  and  a  "basic''  fibre  "acid"  dyes. 
The  above  is  a  brief  outline  of  the  adsorption  theory  of  dyeing, 
but  the  process  in  any  particular  case  is  doubtless  complicated 
by  other  factors,  and  at  present  is  far  from  being  understood. 

It  has  been  suggested  by  Bayliss  and  others  that  adsorption 

1  Zeitsch.  physikal  Chem.,  1909,  67,  538. 


332        OUTLINES  OF  PHYSICAL  CHEMISTRY 

plays  an  important  part  in  enzyme  reactions;  the  substance 
acted  on  is  first  adsorbed  by  the  colloidal  enzyme  particles  and 
chemical  change  follows.  The  interesting  fact  that  colloids 
such  as  gelatine  increased  the  stability  of  suspension  colloids 
such  as  silver  bromide  or  colloidal  gold  towards  electrolytes, 
may  also  be  accounted  for  on  the  basis  of  adsorption.  In  the 
case  under  consideration  it  is  assumed  that  the  gelatine  is  ad- 
sorbed as  a  thin  film  on  the  surface  of  the  particles,  so  that  the 
latter  do  not  come  directly  in  contact  with  the  electrolyte.  It 
has  quite  recently  been  shown  that  certain  dyes,  more  parti- 
cularly erythrosine,  also  exert  a  protective  action  on  colloidal 
silver  bromide.  Substances  acting  in  this  way  are  termed 
"  protective  "  colloids. 


CHAPTER  XIII 
THEORIES  OF  SOLUTION 

General — The  nature  of  solutions,1  more  particularly  as 
regards  the  connection  between  their  properties  and  those  of 
the  components,  has  long  been  one  of  the  most  important 
problems  of  chemistry.  It  was  early  recognized  that  the 
properties  of  a  solution  are  very  seldom  indeed  the  mean  of 
the  properties  of  the  components,  Is  must  necessarily  be  the 
case  if  solvent  and  solute  exert  no  mutual  influence.  Thus 
we  know  that  when  two  liquids  are  mixed  either  expansion  or 
contraction  may  occur,  the  boiling-point  of  a  mixture  may  be 
higher  or  lower  than  those  of  either  of  its  components  (p.  88), 
and  a  mixture  of  two  liquids  may  have  a  high  conductivity, 
although  the  components  in  the  pure  condition  are  practically 
non-conductors  (p.  259). 

The  most  obvious  way  of  accounting  for  observations  of  this 
nature  is  to  assume  that  they  are  connected  with  the  formation 
of  chemical  compounds  between  the  two  components  of  the 
solution.  As  a  matter  of  fact,  explanations  of  the  observed 
phenomena  on  these  lines  were  formerly  in  great  favour.  As 
water  was  the  substance  most  largely  used  as  a  component  of 
solutions  (as  solvent),  the  explanation  of  the  properties  of 
aqueous  solutions  on  the  basis  of  formation  of  chemical  com- 
pounds between  water  and  the  solute  was  termed  the  hydrate 
theory  of  solution.  This  theory  appeared  the  more  plausible 

1  For  simplicity,  only  mixtures  of  two  components  will  be  considered  in 
this  chapter. 

333 


334        OUTLINES  OF  PHYSICAL  CHEMISTRY 

as  a  very  large  number  of  hydrates — compounds  of  substances, 
more  particularly  salts,  with  water — are  known  in  the  solid 
state,  thus  showing  that  there  is  undoubtedly  considerable 
chemical  affinity  between  certain  solutes  and  water. 

In  spite  of  the  plausible  nature  of  the  hydrate  theory,  how- 
ever, it  did  not  prove  very  successful  in  representing  the 
properties  of  aqueous  solutions,  and  some  facts  were  soon 
discovered  in  apparent  contradiction  with  it.  Thus,  as  already 
mentioned,  Roscoe  showed  that  the  composition  of  the  mixture 
of  hydrochloric  acid  and  water  with  minimum  vapour  pressure, 
alters  with  the  pressure,  and  therefore  could  not  be  connected 
with  the  formation  of  a  definite  chemical  compound  of  acid 
and  water,  as  had  previously  been  assumed  (p.  90). 

The  development  of  the  electrolytic  dissociation  theory, 
which  has  been  discussed  in  the  previous  chapters,  led  to  a 
considerable  change  of  view  with  regard  to  the  influence  of 
the  solvent  on  the  properties  of  aqueous  solutions.  The  pro- 
perties of  the  solvent  were  to  some  extent  relegated  to  the 
background,1  and  it  was  looked  upon  simply  as  the  medium 
in  which  the  molecules  and  the  ions  of  the  solvent — the  really 
active  things — moved  about  freely.  The  fact  that  such  great 
advances  in  knowledge  have  been  made  by  working  along  those 
lines  naturally  goes  far  to  justify  the  method  of  procedure. 

Within  the  last  few  years,  however,  mainly  as  a  result  of  the 
investigation  of  solutions  in  solvents  other  than  water,  it  has 
come  to  be  recognized  that  the  solvent  may  play  a  more  direct 
part  in  determining  the  properties  of  dilute  solutions  than  some 
chemists  were  formerly  inclined  to  suppose.  Although  the  main 
properties  of  aqueous  solutions  can  be  accounted  for  without 
express  consideration  of  affinity  between  solvent  and  solute,  it 
appears  probable  that  the  latter  effect  must  be  taken  into  con- 

xThe  properties  of  the  solvent  are,  of  course,  all-important  in  deter- 
mining whether  a  substance  becomes  ionised  or  not.  But  it  was  not  found 
necessary  to  take  the  question  of  affinity  into  account  directly,  and  the 
equations  representing  ionic  equilibria  did  not  contain  any  term  referring 
directly  to  the  solvent. 


THEORIES  OF  SOLUTION  335 

sideration  in  order  to  account  for  certain  secondary  phenomena 
(and  possibly  also  in  connection  with  ionisation)  (p.  344). 

In  the  previous  chapters  the  evidence  in  favour  of  the 
electrolytic  dissociation  theory  could  not  be  dealt  with  as  a 
whole,  owing  to  the  fact  that  it  belongs  to  different  branches 
of  the  subject.  In  the  present  chapter  a  short  summary  of  the 
more  important  lines  of  evidence  bearing  on  the  theory  will  be 
given,  and  then  a  brief  account  of  the  investigation  of  solutions 
in  solvents  other  than  water.  Finally,  after  dealing  with  the 
older  hydrate  theory  of  solution,  the  possible  mechanism  of 
electrolytic  dissociation  will  be  considered. 

Evidence  in  Favour  of  the  Electrolytic  Dissociation 
Theory — The  evidence  in  favour  of  the  electrolytic  dissociation 
theory  is  partly  electrical  and  partly  non-electrical.  The  non- 
electrical evidence  goes  to  show  that  there  are  more  particles 
in  dilute  solutions  of  salts,  strong  acids  and  bases,  than  can  be 
accounted  for  on  the  basis  of  their  ordinary  chemical  formulae, 
and  that  in  dilute  solution  the  positive  and  negative  parts  of  the 
molecule  behave  more  or  less  independently.  The  electrical 
evidence  goes  to  show  that  the  particles  which  result  from  the 
splitting  up  of  simple  salt  molecules  are  associated  with  electric 
charges,  either  positive  or  negative. 

The  main  points  are  as  follows : — 

(a)  If  Avogadro's  hypothesis  applies  to  dilute  solutions, 
gram-molecular  (molar)  quantities  of  different  substances,  dis- 
solved in  equal  volumes  of  the  same  solvent,  must  exert  the 
same  osmotic  pressure.  As  a  matter  of  experiment,  salts,  strong 
acids  and  bases  exert  an  osmotic  pressure  greater  than  that  due 
to  equivalent  quantities  of  organic  substances  (p.  124).  The 
electrolytic  dissociation  theory  accounts  for  this  on  the  same 
lines  as  the  accepted  explanation  for  the  abnormally  high 
pressure  exerted  by  ammonium  chloride;  it  postulates  that 
there  are  actually  more  particles  present  than  that  calculated 
according  to  the  ordinary  molecular  formula. 

(£)  Many  of  the  properties  of  dilute  salt  solutions  are  additive, 


336        OUTLINES  OF  PHYSICAL  CHEMISTRY 

that  is,  they  can  be  represented  as  the  sum  of  two  independent 
factors,  one  due  to  the  positive,  the  other  to  the  negative  part 
of  the  molecule.  This  is  true  of  the  density,  the  heat  of 
formation  of  salts  (p.  148),  the  velocity  of  the  ions  (p.  251), 
the  viscosity,  and  more  particularly  of  the  ordinary  chemical 
reactions  for  the  "base"  and  "acid"  as  used  in  analysis 
(p.  306). 

A  very  striking  illustration  of  the  independence  of  the  pro- 
perties of  one  of  the  ions  in  dilute  solution  on  the  nature  of 
the  other  is  the  colour  of  certain  salt  solutions,  investigated 
by  Ostwald.  He  examined  the  solutions  of  a  large  number  of 
metallic  permanganates,  and  found  that  all  had  exactly  the  same 
absorption  spectra.  This  is  exactly  what  is  to  be  expected 
according  to  the  electrolytic  dissociation  theory,  the  effect  being 
exerted  by  the  permanganate  ion.  Similarly,  salts  of  rosaniline 
with  a  large  number  of  acids  in  very  dilute  solution  gave 
identical  absorption  spectra  (due  to  the  rosaniline  cation)  but 
rosaniline  itself,  which  is  very  slightly  ionised,  gave  a  quite 
different  spectrum. 

Too  much  stress  should  not  be  laid  on  this  criterion,  how- 
ever, as  certain  properties,  e.g.,  molecular  volumes  of  organic 
compounds  (p.  61)  and  the  heat  of  combustion  of  hydro- 
carbons (p.  148),  are  more  or  less  additive,  although  nothing 
in  the  nature  of  ionisation  is  here  assumed. 

(c)  The  magnitudes  of  the  degree  of  dissociation,  calculated 
on  two  entirely  independent    assumptions — (i)    that  the  con- 
ductivity of  solutions  is  due  to  the  ions  alone,  and  not  to  the 
non-ionised  molecules  or  to  the  solvent;  (2)  that  the  abnormal 
osmotic  pressures  shown  by  aqueous  solutions  of  electrolytes 
are  due  to  the  presence  of  more  than  the  calculated  number 
of  particles    owing   to   ionisation — show    excellent   agreement 
(p.  263). 

(d)  The   heat    of  neutralization    of  molar   solutions  of  all 
strong  monoacidic  bases  by  strong  monobasic  acids  is  13,700 
calories,  in  excellent  agreement  with  the  value  for  the  reaction 
H-  +  OH'  =  H2O,  calculated  by    van't  HofFs  formula  from 


THEORIES  OF  SOLUTION  337 

Kohlrausch's  measurements  of  the  change  of  conductivity  of 
pure  water  with  the  temperature  (p.  295). 

(e)  The  results  obtained  by  four  entirely  independent 
methods  for  the  degree  of  ionisation  of  water  are  in  striking 
agreement,  in  spite  of  the  fact  that  the  assumed  ionisation  is 
very  minute  (p.  294). 

(/)  The  formula  for  the  variation  of  electrical  conductivity 
with  dilution,  obtained  by  application  of  the  law  of  mass  action 
to  the  assumed  equilibrium  between  ions  and  non-ionised  mole- 
cules in  solution,  represents  the  experimental  results  in  the  case 
of  weak  electrolytes  with  the  highest  accuracy  (p.  267). 

(g)  As  shown  in  the  next  chapter,  our  present  views  as  to 
the  origin  of  differences  of  potential  at  the  junction  of  two 
solutions,  or  at  the  junction  of  a  metal  and  a  solution  of  one 
of  its  salts,  are  based  on  the  osmotic  and  electrolytic  dissocia- 
tion theories,  and  the  good  agreement  between  observed  and 
calculated  values  goes  far  to  justify  the  assumptions  on  which 
the  formulae  are  based. 

Many  other  illustrations  of  the  utility  of  the  electrolytic 
dissociation  theory  are  mentioned  throughout  the  book. 

Ionisation  in  Solvents  other  than  Water1 — In  ac- 
cordance with  the  mode  in  which  the  subject  has  developed, 
we  have  up  to  the  present  been  mainly  concerned  with 
aqueous  solutions,  and  the  justification  for  this  order  of 
treatment  is  that  the  relationships  in  aqueous  solution  are 
often  very  simple  in  character,  as  shown  in  detail  in  the  last 
chapter.  The  importance  of  a  theory  would,  however,  be 
much  less  if  it  only  applied  to  aqueous  solutions,  and  it  is 
therefore  satisfactory  that  in  recent  years  a  very  large  number 
of  liquids,  both  organic  and  inorganic,  have  been  employed  as 
solvents. 

Although  the  progress  so  far  made  in  this  branch  of  know- 
ledge is  not  great,  the  available  data  appear  to  show  that 

1  Carrara,  Ahrens'  Sammlung,  1908,  12,  404. 
22 


338       OUTLINES  OF  PHYSICAL  CHEMISTRY 

the  rules  which  have  been  found  to  hold  for  aqueous  solutions 
also  apply  to  non-aqueous  solutions?- 

Some  solvents,  such  as  ethyl  and  methyl  alcohol,  acetic  acid, 
formic  acid,  hydrocyanic  acid  and  liquefied  ammonia,  form  solu- 
tions of  fairly  high  conductivity  with  salts  and  other  substances ; 
these  are  termed  dissociating  solvents  (p.  123).  Solutions  in 
certain  other  solvents,  such  as  benzene,  chloroform  and  ether, 
are  practically  non-conductors,  and  the  solutes  are  often  present 
in  such  solutions  in  the  form  of  complex  molecules.  These 
solvents  are  therefore  often  termed  associating  solvents,  but  it 
is  not  certain  whether  they  actually  favour  association  or 
polymerization  of  the  solute,  or  have  only  a  slight  effect  in 
simplifying  the  naturally  polymerized  solute. 

It  is  natural  to  inquire  whether  there  is  any  connection 
between  the  ionising  power  of  a  solvent  and  any  of  its  other 
properties.  It  has  been  found  that  as  a  general  rule  those 
solvents  with  the  greatest  dissociating  power  have  high 
dielectric  constants  (p.  225)  (J.  J.  Thomson,  Nernst,  1893). 
This  observation  is  easily  understood  when  it  is  remembered 
that  the  attraction  between  contrary  electric  charges  is  inversely 
proportional  to  the  dielectric  constant  of  the  medium  ;  it  is 
evident  that  the  existence  of  the  ions  in  a  free  condition  must 
be  favoured  by  diminishing  the  attraction  between  the  contrary 
charges.  The  dielectric  constants  of  a  few  important  solvents 
(liquids  and  liquefied  gases)  at  room  temperature  are  given  in 
the  table. 


Solvent. 

D.C. 

Solvent. 

D.C. 

Hydrocyanic  acid 

•       95 

Acetone 

21 

Water        . 

.       81 

Pyridine 

20 

Formic  acid 

•       57 

Ammonia 

l6'2 

Nitro  benzene 

•       36-5 

Sulphur  dioxide 

•           137 

Methyl  alcohol  . 

32-5 

Chloroform 

5*2 

Ethyl  alcohol    . 

.       21-5 

Benzene 

2-3 

lCf.  Walden,  Zeitsch.  phys.ikal.Chem.,  1907,  58,  479. 


THEORIES  OF  SOLUTION  339 

The  data  are  not  usually  available  for  an  accurate  comparison 
of  the  dissociating  power  of  a  solvent  with  its  dielectric  constant, 
as  the  values  of  /^co  for  electrolytes  in  solvents  other  than  water 
have  been  determined  in  only  a  few  cases.  It  is  important  to 
remember  that  a  comparison  of  the  conductivities  of  solutions 
of  the  same  concentration  in  different  solvents  is  in  no  sense  a 
measure  of  the  respective  ionising  powers  of  the  solvents,  as 
the  conductivity  also  depends  on  the  ionic  velocity  (p.  252). 
The  available  data  are,  however,  sufficient  to  show  that 
although  there  is  parallelism,  there  is  not  direct  proportionality 
between  dielectric  constant  and  ionising  power.  There  appears 
also  to  be  some  connection  between  the  degree  of  association 
of  the  solvent  itself  and  its  ionising  power.  The  examples 
already  given  show  that  water,  the  alcohols  and  fatty  acids, 
which  are  themselves  complex,  are  the  best  ionising  solvents. 
There  are,  however,  exceptions  to  this  as  to  all  other  rules 
in  this  section ;  liquefied  ammonia,  though  apparently  not 
polymerized,  is  a  good  ionising  solvent. 

Briihl  has  suggested  that  the  ionising  power  of  a  solvent 
depends  on  what  he  calls  subsidiary  valencies  (the  "  free 
affinity "  of  Armstrong) ;  in  other  words,  the  best  ionising 
solvents  are  those  which  are  un saturated.  It  is  by  no  means 
improbable  that  the  dielectric  constant,  the  degree  of  poly- 
merization, and  the  degree  of  unsaturation  of  a  solvent  are 
in  some  way  connected. 

The  ionising  power  of  a  solvent  may  be  partly  of  a  physical 
and  partly  of  a  chemical  nature.  The  effect  of  a  high  dielectric 
constant  would  appear  to  be  mainly  physical,  on  the  other 
hand,  if  the  effect  of  a  solvent  depends  on  dts  unsaturated 
character,  it  would  most  likely  be  chemical  in  character. 

The  Old  Hydrate  Theory  of  Solution l — As  already  men- 
tioned, attempts  have  been  made  to  account  for  the  properties 
of  aqueous  solutions  of  electrolytes  on  the  basis  of  chemical 
combination  between  solvent  and  solute.  Among  those  who 

1  Pickering,  Watts's  Dictionary  of  Chemistry,  Article  "  Solution " ; 
Arrhenius,  Theories  of  Chemistry  (Longmans,  1907),  chap.  iiiv 


340        OUTLINES  OF  PHYSICAL  CHEMISTRY 

have  supported  this  view  of  solution,  the  names  of  Mendeleeff, 
Pickering,  Kahlenberg *  and  Armstrong 2  may  be  mentioned. 

Mendeleeff  made  a  number  of  measurements  of  the  densities 
of  mixtures  of  sulphuric  acid  and  water,  and  drew  the  con- 
clusion that  the  curve  representing  the  relation  between  density 
and  composition  is  made  up  of  a  number  of  straight  lines 
meeting  each  other  at  sharp  angles,  the  points  of  discontinuity 
corresponding  with  definite  hydrates,  for  example,  H2SO4,  H2O ; 
H2SO4,  2H2O  ;  H2SO4,  6H2O  and  H2SO4,  i5oH2O.  Pickering 
repeated  MendeleefFs  experiments,  and  found  no  sudden  breaks 
in  the  density  curve,  but  only  changes  in  direction  at  certain 
points.  He  also  drew  the  conclusion  that  these  points  cor- 
respond with  the  composition  of  definite  compounds  of  the 
acid  and  water. 

In  this  connection  it  may  be  recalled  that  the  curve  obtained 
by  plotting  the  electrical  conductivity  of  mixtures  of  sulphuric 
acid  and  water  against  the  composition  (p.  259)  shows  two  dis- 
tinct minima,  at  100  per  cent,  and  84  per  cent,  of  sulphuric 
acid  respectively,  corresponding  with  the  compounds  H2SO4 
(SO3,  H2O)  and  H2SO4,  H2O  respectively.  As  it  is  a  general 
rule  that  the  electrical  conductivity  of  pure  substances  is  small, 
there  is  little  reason  to  doubt  that  the  84  per  cent,  solution 
consists  mainly  of  the  monohydrate  H2SO4,  H2O.  The  con- 
tention of  Mendeleeff  and  Pickering,  that  aqueous  solutions  of 
sulphuric  acid  contain  compounds  of  the  components,  is  thus 
partially  confirmed  by  the  electrical  evidence. 

There  is  not  much  reason  to  doubt  the  truth  of  the  first 
postulate  of  the  hydrate  theory,  that  in  many  cases  hydrates 
are  present  in -aqueous  solution.  The  hydrates  are,  however, 
in  all  probability  more  or  less  dissociated  in  solution,  and 
it  will  not  usually  be  possible  to  determine  the  presence  of 
definite  hydrates  from  the  measurement  of  physical  properties. 

1  For  a  summary  of  Kahlenberg's  views  on  Solution,  see  Trans.  Faraday 
Soc.,  1905,  i,  42. 

2  Proc.  Roy.  Soc.,  1908,  81  A,  80-95. 


THEORIES  OF  SOLUTION  341 

It  is  probable  that  in  general  the  equilibria  are  somewhat  com- 
plicated, and  are  displaced  gradually  by  dilution  in  accordance 
with  the  law  of  mass  action,  which  accounts  for  the  experimental 
fact  that  in  general  the  properties  of  aqueous  solutions  alter 
continuously  with  composition. 

Having  proved  the  existence  of  hydrates  in  salt  solutions  in 
certain  cases,  Pickering l  attempted  to  account  for  the  properties 
of  aqueous  solutions  (osmotic  pressure,  electrical  conductivity, 
etc.)  on  the  basis  of  association  alone,  but  as  his  views  have  not 
met  with  much  acceptance,  a  reference  to  them  will  be  sufficient 
for  our  present  purpose.  Kahlenberg,2  who  has  carried  out 
many  interesting  experiments  in  solvents  other  than  water,  re- 
gards the  electrolytic  dissociation  theory  as  unsatisfactory,  and 
considers  that  the  process  of  solution  is  one  of  chemical  com- 
bination between  solvent  and  solute.  Armstrong  has  also 
attempted  to  account  for  the  properties  of  aqueous  solutions 
on  the  basis  of  association  between  solvent  and  solute.3 

Although,  as  we  have  seen,  cases  are  known  in  which  a 
maximum  or  minimum  or  a  change  in  the  direction  of  a  curve 
may  correspond  more  or  less  completely  with  the  formation  of 
a  compound  between  the  two  components  of  a  homogeneous 
solution,  this  does  not  by  any  means  always  hold.  It  has 
already  been  pointed  out  that  the  curve  representing  the  varia- 
tion of  the  electrical  conductivity  of  mixtures  of  sulphuric  acid 
and  water  with  the  composition  has  a  maximum  at  30  per  cent, 
of  acid  (p.  259).  As  the  pure  liquids  are  practically  non- 
conductors, whilst  the  mixtures  conduct,  there  must  necessarily 
be  a  concentration,  between  o  and  100  per  cent,  acid,  at  which 
the  conductivity  attains  a  maximum  value.  This  maximum  will 
clearly  have  no  reference  to  the  formation  of  a  chemical 
compound  between  sulphuric  acid  and  water,  since  this  would 
tend  to  diminish  the  conductivity. 

Similar  considerations  appear   to   apply  for  other  physical 

lLoc.cit.  zLoc.cit. 

3Loc.  cit.,  also  Encyc.  Britannica,  loth  Edition,  vol.  xxvi.,  p.  741. 


342       OUTLINES  OF  PHYSICAL  CHEMISTRY 

properties  which  attain  a  maximum  value  for  binary  mixtures. 
The  curve  representing  the  variation  of  the  viscosity  (internal 
friction)  of  mixtures  of  alcohol  and  water  with  composition 
shows  a  maximum  at  o°  for  a  mixture  containing  36  per  cent, 
of  alcohol,  corresponding  with  the  composition  (C2H5OH)2, 
9H2O,  and  it  has  therefore  been  suggested  that  the  solution 
consists  mainly  of  this  hydrate.  At  1 7°,  however,  the  mixture 
of  maximum  viscosity  contains  42  per  cent.,  and  at  55°  rather 
more  than  50  per  cent,  of  alcohol.  The  last-mentioned  mixture 
corresponds  with  the  composition  (C2H5OH)2,  5H2O.  If  we 
accept  the  association  view  of  this  phenomenon,  it  must  be 
assumed  that  at  o°  the  solution  contains  a  hydrate  (C2H5OH)2, 
9H2O,  and  at  55°  a  hydrate  (C2H5OH)2,  5H2O,  and  that  at 
intermediate  temperatures  the  hydrates  with  6,  7  and  8  H2O 
exist— which  does  not  appear  very  probable. 

Now,  Arrhenius  has  shown  that  as  a  general  rule  the  addition 
of  a  non-electrolyte  raises  the  viscosity  of  water.  Therefore,  if 
the  viscosity  of  the  non-electrolyte  is  less  than,  or  only  slightly 
exceeds  that  of  water,  the  curve  obtained  by  plotting  viscosity 
against  the  composition  of  the  mixture  must  necessarily  attain 
a  maximum  at  some  intermediate  point.  Why  mixtures  of  two 
liquids  have  often  a  higher  viscosity  than  either  of  the  pure 
liquids  is  not  known,  no  general  agreement  having  yet  been 
reached  on  this  and  allied  questions.1 

Mechanism  of  Electrolytic  Dissociation.  Function 
of  the  Solvent — The  fundamental  difference  between  associa- 
tion theories  of  solution,  as  discussed  in  the  last  section,  and 
the  electrolytic  dissociation  theory  is  that  the  advocates  of 
association  entirely  reject  the  postulate  of  the  independent 
existence  of  the  ions.  As,  however,  the  different  theories  of 
association  unaccompanied  by  ionisation  have  so  far  proved 
quite  inadequate  to  account  quantitatively  for  the  behaviour 
of  aqueous  solutions,  whilst  the  electrolytic  dissociation  theory 
not  only  affords  a  satisfactory  quantitative  interpretation  of  the 

1  Compare  Senter,  Proc.  Chem.  Soc.,  1909,  292.  For  evidence  in 
favour  of  the  association  view  of  this  phenomenon,  compare  Dunstan, 
Trans.  Chem.  Society,  1907,  91,  83 ;  Dunstan  and  Thole,  ibid.,  1909,  95, 
1556. 


THEORIES  OF  SOLUTION  343 

more  important  phenomena  observed  in  solutions  of  electrolytes 
(chap,  x.),  but  has  led  to  discoveries  of  the  most  fundamental 
importance  for  chemistry,  it  is  not  surprising  that  the  electro- 
lytic dissociation  theory  has  now  met  with  practically  universal 
acceptance.  It  is  very  likely  that  as  a  result  of  further  investi- 
gation the  theory  may  require  modification  in  some  subsidiary 
respects,  but  its  general  validity  appears  no  longer  doubtful. 

We  are  now  in  a  position  to  discuss  the  possible  mechanism 
of  electrolytic  dissociation,  i.e.,  the  factors  concerned  in  the 
conversion  of  a  non-ionised  salt  into  ions  when  dissolved  in 
water  or  other  ionising  solvent.  In  this  connection  two  points 
of  importance  must  be  kept  in  mind :  (i)  There  is  a  more 
or  less  complete  parallelism  between  the  ionising  power  of  a 
solvent  and  certain  of  its  properties,  such  as  the  magnitude  of 
the  dielectric  constant  and  its  degree  of  polymerization  ;  (2)  the 
sum  of  the  energy  associated  with  the  ions  is  usually  not  very 
different  from  that  associated  with  the  non-ionised  molecules 
in  solution.  The  first  point  has  already  been  fully  dealt  with. 
The  energy  relations  in  the  process  of  ionisation  will  now  be 
briefly  considered. 

As  such  elements  as  potassium  and  chlorine  give  out  a  large 
amount  of  heat  when  they  combine  to  form  potassium  chloride, 
it  seems  at  first  sight  as  if  the  splitting  up  of  potassium  chloride 
into  K-  and  Cl'  ions  must  absorb  a  large  amount  of  heat. 
Although  it  has  to  be  borne  in  mind  that  the  salt  is  not  split 
up  into  its  component  elements  (a  process  which  certainly 
absorbs  a  large  amount  of  heat)  but  into  K-  and  Cl'  ions,  of 
the  energy  content  of  which  little  is  known,  it  is  nevertheless 
probable  that  the  process  of  ionisation  does  involve  a  taking  up 
of  energy,  as  the  following  considerations  show. 

It  has  already  been  pointed  out  that  the  heat  of  ionisation 
(the  heat  given  out  when  a  mol  of  a  non-ionised  salt  in 
solution  is  completely  ionised)  may  be  calculated  by  the  van't 
Hoff  formula  connecting  heat  given  out  with  displacement  of 
equilibrium,  when  the  equilibrium  at  two  near  temperatures  is 


344       OUTLINES  OF  PHYSICAL  CHEMISTRY 

known  (p.  285).  The  available  data  indicate  that  the  heat  of 
ionisation  is  small,  and  may  be  positive  or  negative.  According 
to  Arrhenius,  the  energy  equation  for  the  ionisation  of  dissolved 
potassium  chloride  is  as  follows — 

KC1  =  K-  +  Cl'  +  362  cal., 

the  heat  of  ionisation  being  thus  exceedingly  small.  On  the 
other  hand,  when  potassium  chloride  is  formed  from  its  elements, 
105,600  cal.  are  given  out  for  gram-equivalent  quantities,  hence 
the  energy  equation  for  the  decomposition  of  potassium  chloride 
into  metallic  potassium  and  free  chlorine  is 

KC1  =  —  +  ^  -  105,600  cal. 

The  further  separation  of  metallic  potassium  and  free  chlorine 
into  uncharged  atoms  would  probably  absorb  still  more  heat,  so 
that  the  reaction 

KC1  =  K  +  Cl 

must  absorb  a  very  large  amount  of  heat.  On  the  other  hand, 
we  have  just  seen  that  in  the  splitting  up  of  the  salt  into  charged 
atoms — the  ions — a  little  heat  is  actually  given  out.  It  seems, 
therefore,  that  the  process  of  ionisation  must  be  attended  by 
some  exothermic  reaction,  which  more  than  compensates  for 
the  heat  presumably  absorbed  in  splitting  up  the  molecules. 

Up  to  the  present  no  definite  conclusion  has  been  arrived  at 
as  to  the  source  of  the  energy  in  question.  Some  of  the  possi- 
bilities are  as  follows  : — 

(a)  As  the  molecule  splits  up  into  particles  charged  with 
electricity,  the  energy  in  question  may  come  from  some  inter- 
action between  electricity  and  matter.     On  this  point  nothing 
can  be  said  with  certainty  in  the  present  state  of  our  knowledge.1 

(b)  The  energy  may  result  mainly  from  combination  between 
the  ions  and  water.     Van  der  Waals2   (1891)  has  suggested 
that  ionisation  in  aqueous  solution  is  essentially  a  hydration 

1 C/.  Ostwald,  Fitzgerald,  British  Association  Reports,  1890. 
2  Zeitsch.  physikal  Chem.,  1891,  8,  215.      Cf.  Bousfield  and   Lowry, 
Trans.  Faraday  Society,  1907,  3,  i. 


THEORIES  OF  SOLUTION  345 

process  ;  he  considers  that  it  is  the  affinity  of  the  ions  for  the 
solute  which  effects  the  break-up  of  the  molecule,  and  that  the 
energy  required  for  ionisation  comes  from  the  heat  of  hydration 
of  the  ions. 

(^)  Dutoit,  arguing  from  the  parallelism  between  the  poly- 
merization of  the  solute  and  its  ionising  power,  and  assuming 
that  the  process  of  solution  is  attended  with  partial  simplification 
of  the  solute  molecules,  has  suggested  that  the  energy  is  ob- 
tained from  the  depolymerization  in  question. 

The  suggestion  of  van  der  Waals  finds  a  certain  amount  of 
support  from  recent  investigations  on  solvents  other  than  water. 
Carrara  l  considers  that  the  ions  are  produced  as  a  consequence 
of  the  chemical  affinity  between  the  two  parts  of  the  molecule 
and  the  solute,  and  that  in  consequence  of  the  high  dielectric 
constant  in  ionising  media,  they,  along  with  their  associated 
solvent  molecules,  are  kept  in  the  ionic  condition  once  they 
are  formed. 

It  should,  however,  be  remembered  that  this  suggestion  as 
to  the  mechanism  of  ionisation,  although  interesting  and 
suggestive,  is  little  more  than  a  plausible  speculation,  and  that 
there  are  many  points  about  this  process  which  are  very  im- 
perfectly understood. 

Hydration  in  Solution2 — In  recent  years  the  view  that 
the  ions  are  hydrated  to  a  greater  or  less  extent  in  aqueous 
solutions  of  electrolytes  has  gained  ground  very  considerably, 
but  it  cannot  be  said  that  the  evidence  is  very  conclusive. 
Perhaps  the  most  definite  positive  result  is  the  observation  of 
Kohlrausch,  that  the  influence  of  temperature  on  the  electro- 
lytic resistance  of  dilute  solutions  of  salts  approximates  to  the 

lLoc.  cit.,  p.  417. 

2  For  a  general  discussion  on  hydration  in  solution,  see  Trans.  Faraday 
Soc.,  1907,  3,  i.  For  summaries  of  the  methods  which  have  been  suggested 
for  determining  the  degree  of  hydration  in  solution,  see  Baur,  Ahrens' 
Sammlung,  1903,  8,  466  ;  Senter,  Science  Progress,  1907,  i,  386  ;  Trans. 
Faraday  Soc.,  1907,  3,  24.  Cf.  also  Philip,  Trans.  Chem.  Soc.,  1907, 
9L  7". 


346       OUTLINES  OF  PHYSICAL  CHEMISTRY 

temperature  coefficient  of  the  mechanical  friction  of  water. 
This  observation  at  once  becomes  intelligible  if  it  is  assumed 
that  the  ions  are  surrounded  by  water  molecules,  as  the  resist- 
ance to  movement  of  the  water-coated  ions  would  then  be  the 
frictional  resistance  of  water  against  water. 

Many  attempts  have  been  made  to  determine  the  degree 
of  hydration  both  in  solutions  of  electrolytes  and  of  non- 
electrolytes,  but  the  results  are  very  uncertain.  If  each  ion 
becomes  associated  with  a  number  of  water-molecules,  the 
total  number  of  solute  particles  will  not  be  altered,  and  the 
osmotic  pressure,  lowering  of  freezing-point,  etc.,  will  not  be 
directly  affected.  If,  however,  it  is  assumed  that  only  the  un- 
bound part  of  the  solvent  can  really  act  as  solvent,  the  effect  of 
association  will  be  to  diminish  the  "free  "  solvent,  and  there- 
fore the  effective  concentration  of  the  solution — the  ratio  of 
solute  to  free  solvent — will  be  increased,  and  the  lowering 
of  freezing-point  will  be  greater  than  the  calculated  value. 
Unless,  however,  the  average  hydration  of  the  solute  is  very 
great,  the  effect  in  question  will  only  be  considerable  in  con- 
centrated solutions,  under  which  circumstances  freezing-point 
and  other  determinations  often  give  unsatisfactory  results 
(p.  122). 

For  our  present  purpose,  it  will  be  sufficient  to  refer  to  the 
method  for  determining  the  degree  of  hydration  of  electrolytes 
suggested  by  H.  C.  Jones,  as  this  author  and  his  co-workers 
have  collected  much  valuable  experimental  material  which  will 
be  serviceable  in  attacking  some  of  the  yet  unsolved  problems 
of  solution.  The  method  depends  on  the  observation  that  in 
many  cases  the  experimental  freezing-point  depression  is  greater 
than  the  value  to  be  expected  from  the  degree  of  dissociation 
of  the  solute,  and  Jones  assumes  that  this  is  due  to  the  associa- 
tion of  part  of  the  solvent  with  the  solute,  so  that  the  depression 
actually  observed  is  that  corresponding  with  a  more  concen- 
trated solution,  as  described  in  the  previous  paragraph.  If  the 
true  depression  in  the  absence  of  association  (when  the  whole 


THEORIES  OF  SOLUTION  347 

of  the  solute  is  "  free  ")  can  be  calculated,  the  mode  of  esti- 
mating the  hydration  will  be  evident,  but  this  is  just  where  the 
weakness  of  the  method  lies.  Jones  calculates  the  theoretical 
depression  for  a  particular  dilution  from  conductivity  measure- 
ments at  o°,  the  values  of  /xe  and  ^  being  determined  directly. 
To  do  this  it  has  to  be  assumed  that  the  exact  degree  of 
dissociation  can  be  obtained  from  conductivity  measurements, 
which  is  not  the  case  for  concentrated  solutions,1  although  very 
nearly  so  for  dilute  solutions  (p.  261),  and  further,  that  the 
van't  Hoff-Raoult's  law  holds  strictly  for  concentrated  solu- 
tions, which  is  highly  improbable  (p.  122).  Jones  himself, 
while  admitting  that  several  of  his  assumptions  are  not  strictly 
valid,  considers  that  a  nearer  approximation  to  the  true  values 
for  the  degree  of  hydration  is  obtained  by  his  method  than  by 
any  other  method  so  far  suggested.  While  this  may  be  the 
case,  we  have  no  means  of  knowing  the  magnitude  of  the  error 
thus  introduced,  and  the  true  values  for  the  degree  of  hydration 
may  be  very  different  from  those  given  by  Jones  and  his  co- 
workers.  Moreover,  the  observed  irregularities  in  freezing- 
point  depression  may  be  due,  in  part  at  least,  to  some  cause 
other  than  hydration.  The  present  position  of  the  subject 
may  be  summed  up  in  the  statement  that  while  there  is  a 
good  deal  of  evidence  in  favour  of  hydration  in  solution,  very 
little  is  known  on  the  subject  with  certainty  from  a  quantitative 
point  of  view. 

1  The  uncertainty  in  the  case  of  concentrated  solutions  arises  from 
the  difficulty  of  distinguishing  between  the  effects  of  alteration  of 
viscosity  and  of  alteration  of  the  degree  of  dissociation  on  the  electrical 
conductivity  (p.  261). 


CHAPTER  XIV 
ELECTROMOTIVE  FORCE 

The  Daniell  Cell.  Electrical  Energy— The  Daniell 
cell  consists  essentially  of  a  large  beaker  or  other  vessel,  con- 
taining a  small  porous  cell.  In  the  outer  vessel,  surrounding 
the  porous  cell,  is  a  solution  of  zinc  sulphate  in  which  dips  a 
rod  of  zinc,  and  the  porous  pot  contains  a  solution  of  copper 
sulphate,  in  which  dips  a  plate  of  copper.  When  the  copper 
plate  is  connected  to  the  zinc  by  a  wire,  an  electric  current 
flows  through  the  wire.  As  positive  electricity  passes  in  the 
wire  from  copper  to  zinc,  the  copper  is  termed  the  positive, 
the  zinc  the  negative  pole.  An  examination  of  the  cell  will 
show  that  when  the  current  is  flowing,  zinc  is  being  dissolved  at 
the  negative  pole,  and  copper  is  being  deposited  on  the  positive 
pole.  If,  instead  of  copper  sulphate,  the  porous  pot  contains 
dilute  sulphuric  acid,  hydrogen  is  given  off  at  the  surface  of 
the  copper  when  the  zinc  and  copper  are  connected.  It  is, 
therefore,  clear  that  the  chemical  change  which  gives  rise  to 
the  current  is  the  dissolving  of  zinc  in  sulphuric  acid,  repre- 
sented by  the  equation  Zn  +  H2SO4  =  ZnSO4  +  H2,  and  that 
in  the  Daniell  cell  the  hydrogen  is  got  rid  of  by  reducing 
copper  sulphate  in  the  porous  pot,  the  change  being  repre- 
sented by  the  equation  CuSO4  -^  H2  =  H2SO4  +  Cu.  Com- 
bining the  two  equations,  the  chemical  changes  taking  place 
while  a  Daniell  cell  is  working  are  represented  by  the  equation 

Zn  4-  CuSO4  =  ZnSO4  +  Cu, 
which  may  be  written 

Zn  +  Cu-  +  SO4"  =  Zn-  +  SO4"  +  Cu, 
348 


ELECTROMOTIVE  FORCE  349 

or  more  concisely, 

Zn  +  Cu"  =  Zn"  +  Cu, 

that  is,  zinc  changes  from  the  metallic  to  the  ionic  form,  and  at 
the  same  time  copper  changes  from  the  ionic  to  the  metallic 
form. 

The  Daniell  cell  may  be  looked  upon  as  a  machine  for  the 
conversion  of  chemical  to  electrical  energy,  and  it  is  of  great 
interest  to  inquire  whether  chemical  energy  is  transformed  into 
the  equivalent  amount  of  electrical  energy,  or  whether  other 
kinds  of  energy,  such  as  heat,  are  also  produced  in  the  cell. 
This  question  can  at  once  be  settled  by  determining  the  heat 
equivalent,  in  calories,  of  the  chemical  energy  transformed 
when  i  mol  of  copper  in  solution  is  displaced  by  zinc,  and 
comparing  it  with  the  electrical  energy  (measured  in  calories) 
obtained  during  the  process. 

From  Thomsen's  measurements  (p.  144)  the  displacement  of 
i  mol  of  copper  in  dilute  solution  by  zinc  is  associated  with  a 
heat  development  of  50,130  calories.  The  electrical  energy  in 
volt-coulombs  is,  as  has  already  been  pointed  out,  the  product 
of  the  electromotive  force  E  in  volts  and  the  quantity  of  elec- 
tricity in  coulombs.  E  for  the  Daniell  cell  is  about  i  '09  volts 
at  room  temperature.  From  Faraday's  law  we  know  further 
that  the  liberation  of  a  gram-equivalent  of  positive  or  negative 
ions  is  associated  with  the  passage  of  96,540  coulombs,  hence, 
as  zinc  and  copper  are  bivalent,  the  reaction 

Zn  +  Cu"  =  Zn-  +  Cu 

is  associated  with  the  passage  of  2  x  96,540  coulombs.  The 
electrical  energy,  in  calories  (i  volt-coulomb  =  0*2391  calories), 
is  therefore  given  by1 

ECt  =  1*09  x  2  x  96,540  x  o-239i  =  50,380  cal. 

as  compared  with  50,130  calories,  the  heat  equivalent  of  the 
chemical  change  which  has  taken  place  in  the  cell.  The  exceJ- 
lent  agreement  between  observed  and  calculated  values  shows 
that  in  this  case  the  assumption  that  the  chemical  energy  is 

1  C  is  the  current,  t  the  time  and  C*  therefore  the  quantity  of  elec- 
tricity. 


350       OUTLINES  OF  PHYSICAL  CHEMISTRY 

transformed  completely  to  electrical  energy  is  approximately 
fulfilled. 

It  should  be  remembered  that  in  an  actual  cell  other  chemical 
changes  may  accompany  the  primary  ones ;  for  example,  those 
giving  rise  to  the  so-called  E.M.F.  of  polarization  (p.  373). 
In  comparing  the  heat  equivalent  of  the  main  chemical  action 
taking  place  in  the  cell  with  the  electrical  energy  obtained, 
such  changes  must,  of  course,  be  allowed  for.  In  the  Daniell 
cell,  however,  there  is  no  polarization,  and  the  only  reaction 
which  takes  place  to  any  appreciable  extent  is  the  displacement 
of  copper  by  zinc,  as  has  already  been  assumed.  In  this  chapter 
we  are  mainly  concerned  with  such  non-polarizable  cells. 

On  account  of  the  excellent  agreement  between  the  amount 
of  chemical  energy  expended  and  the  electrical  energy  generated 
in  the  Daniell  cell,  it  was  at  first  thought  that  the  transformation 
of  chemical  to  electrical  energy  in  all  cells  is  practically  com- 
plete, but  further  investigation  showed  that  this  is  by  no  means 
always  the  case.  As  indicated  above,  the  question  can  readily 
be  investigated  for  a  non-polarizable  element  by  comparing  the 
heat  equivalent,  Q,  of  the  chemical  change  taking  place  in 
the  element  with  the  electrical  energy  generated  while  known 
quantities  of  the  reacting  substances  are  being  transformed. 
The  electrical  energy  may  conveniently  be  measured  as  follows. 
The  poles  of  the  cell  are  connected  by  a  thin  wire  of  high  re- 
sistance, R.  If  r  is  the  internal  resistance  of  the  cell,  the 
electrical  energy  generated  in  unit  time  is  given  by 

EC  =  C2  (R  +  r). 

Now  R  may  easily  be  made  so  large  compared  with  r  that  the 
amount  of  electrical  energy  converted  to  heat  in  the  cell  is 
negligible  in  comparison  with  that  transformed  in  the  outer  wire. 
If  then  the  current  is  measured  and  R  is  known,  the  quantity  of 
electrical  energy  produced  by  the  cell  in  unit  time  is  known,  and 
hence  that  produced  when  n  x  96,540  coulombs  have  passed 
round  the  circuit.  This  quantity  of  electricity  energy  is  obtained 
during  the  chemical  transformation  of  n  equivalents  of  the  cell 


ELECTROMOTIVE  FORCE  351 

material,  and  may  be  compared  with  Q,  the  heat  given  out 
when  the  chemical  change  takes  place  in  a  calorimeter. 

When  a  Daniell  cell  is  examined  in  this  way,  it  is  found,  as  has 
already  been  pointed  out,  that  the  electrical  energy  is  practically 
equal  .to  Q,  the  heat  equivalent  of  the  chemical  energy.  There 
are,  however,  elements  in  which  the  electrical  energy  thus  ex- 
pended in  the  outer  wire  is  less  than  the  heat  of  the  reaction  ; 
in  this  case  part  of  the  chemical  energy  is  expended  as  heat  in 
the  cell.  In  other  elements,  however,  the  electrical  energy, 
ECt,  is  actually  greater  than  the  heat  of  'reaction  ,  Q,  so  that  the 
element,  while  working,  takes  heat  from  its  surroundings  and 
transforms  it  into  electrical  energy. 

Relation  between  Chemical  and  Electrical  Energy— 
The  exact  relationship  between  the  chemical  energy  transformed 
and  the  maximum  energy  obtainable  electrically  in  a  reversible 
galvanic  element  can  be  obtained  on  thermodynamical  principles 
by  means  of  a  cyclic  process.  The  formula  expressing  the 
relationship  (Willard  Gibbs,  1878;  Helmholtz,  1882),  usually 
known  as  the  Helmholtz  equation,  is  as  follows  :  — 


nFE  -  Q  =  nFT          .         .         .       (i) 


where  E  is  the  E.M.F.  of  the  cell,  Q  is  the  heat  equivalent  of 
the  chemical  change  for  molar  quantities,  expressed  in  electrical 
units,  F  is  96,540  coulombs,  T  is  the  absolute  temperature  at 
which  the  cell  is  working,  and  n  is  the  valency,  or  the  number 
of  charges  carried  by  a  mol  of  the  substances  undergoing 
change.  By  dE/dT  is  meant  the  rate  of  change  of  the  E.M.F. 
of  the  cell  with  temperature  —  in  other  words,  the  temperature 
coefficient  of  the  E.M.F. 

The  Helmholtz  formula  is  simply  a  direct  application  of  the 
free  energy  equation 

A-U  =  T  .        .        .      (3) 


352        OUTLINES  OF  PHYSICAL  CHEMISTRY 

to  a  chemical  change  taking  place  in  a  galvanic  cell  In  the 
latter  formula,  U  represents  the  total  diminution  of  energy  in  a 
reacting  system,  and  A  is  the  available  or  free  energy,  that  is, 
the  maximum  proportion  of  the  total  change  of  energy,  U,  which 
can  be  transformed  into  work  (p.  151).  In  order  to  obtain 
formula  (i),  Q,  the  heat  of  reaction  measured  calorimetrically, 
is  substituted  for  U  in  the  free  energy  equation,  as  the  heat  of 
reaction  is  equivalent  to  the  total  diminution  of  energy,  U, 
when  no  external  work  is  done.  For  A,  the  free  energy,  we 
substitute  nFE,  which  is,  as  shown  above,  an  expression  for 
the  maximum  energy  obtainable  electrically  for  molar  quantities. 
dA/dT  in  the  free  energy  equation  then  becomes  nFTdE/dT 
(n  and  F  being  constants),  equation  (i)  being  thus  obtained. 
The  equation  should  be  remembered  in  the  second  form. 

From  the  first  form  of  the  Helmholtz  equation,  some  very 
important  conclusions  can  be  drawn  as  to  the  behaviour  of 
reversible  elements  : — 

(a)  If  dE/dT   is    positive,   that   is,   if  the    E.M.F.    of  the 
element  increases  with  temperature,  the  electrical  energy,  nFE 
is  greater  than  the  heat  of  reaction,  Q,  and  the  cell  takes  heat 
from  its  surroundings  while  working. 

(b)  If  dE/dT    is    negative,   that   is,   if  the  E.M.F.   of   the 
element  diminishes  as   the  temperature  rises,  the  heat  of  re- 
action, Q,  is   greater  than  the  electrical  energy,  «FE,  and  the 
cell  warms  while  working. 

(c)  If  the  E.M.F.  does  not  alter  with  change  of  temperature 
(as  is  approximately  the  case  in  a  Daniell  cell),  the  heat  of 
reaction,  Q,  is  equal  to  the  electrical  energy,  and  the  cell  does 
not  alter  in  temperature  while  working. 

(d)  At  absolute  zero,  that  is,  T  =  o,  the  right-hand  side,  and 
therefore  also   the  left-hand  side,  of  equation  (i)  becomes  zero, 
hence  at  the  absolute  zero  the  heat  of  reaction  (diminution  of 
chemical   energy)  is  always  equal  to   the  maximum  electrical 
energy  obtainable  (or  in  general  to  the  free  energy,  rf.  p.  152). 

The    applicability   of  the  Helmholtz  formula   to   chemical 


ELECTROMOTIVE  FORCE  353 

changes  which  can  be  brought  about  reversibly  in  a  galvanic 
element  has  been  proved  experimentally  by  Jahn  and  others. 
As  an  example,  we  will  consider  a  cell  made  up  of  zinc  and 
silver  in  contact  with  solutions  of  the  respective  chlorides.  The 
observed  E.M.F.  of  such  a  cell  at  o°  is  1*015  volts,  and  the 
electrical  energy  in  calories  for  the  transformation  of  i  mol  of 
the  reacting  substances  is  given  by  n¥E  =  roi5  x  96,540  x 
2  x  0*239  =  46,840  calories.  The  heat  of  reaction  (due  to 
the  displacement  of  the  equivalent  amount  of  silver  from  solu- 
tion by  i  mol  of  zinc)  is  52,046  cal.  Hence,  as  the  heat  of 
reaction  is  greater  than  the  electrical  energy,  the  temperature  co- 
efficient of  the  E.M.F.  is  negative,  and  is  given  by  the  formula 


m  Q  _  (46,840  -52,046)  4-184  .  _  I 

dl  nx  1  2  x  96,540  x  273 

per  degree)  in  excellent  agreement  with  the  experimental  value, 
-  0*00040.  As  the  value  of  <?E/dT  is  required  in  volts,  the 
energy  in  the  above  equation  is  necessarily  represented  in  volt- 
coulombs  (calories  x  4*184). 

In  order  further  to  illustrate  the  above  statements,  which  are 
of  fundamental  importance  for  our  work,  they  will  now  be 
repeated  in  a  somewhat  different  form.  The  quantities  of 
energy  given  in  the  following  paragraphs  refer  to  molar 
quantities  throughout. 

When  a  chemical  change  takes  place  without  the  performance 
of  external  work,  the  total  change  of  energy,  U,  is  equal  to  the 
heat  of  reaction,  Q,  measured  in  a  calorimeter. 

When  the  same  reaction  takes  place  in  a  battery  the  poles 
of  which  are  connected  by  a  thin  wire,  the  whole  apparatus, 
including  the  connecting  wire,  being  enclosed  in  a  calorimeter, 
the  heat  developed  in  the  latter  is  again  Q  for  molar  quantities 
transformed,  the  electrical  energy  in  the  connecting  wire  being 
degraded  to  heat. 

When  the  cell  is  in  the  calorimeter,  and  the  thin  connecting 
wire  outside,  there  are  three  possible  cases  :— 

(a)  If  the  heat  of  reaction,  Q,  is  equal  to  the  maximum 
23 


354       OUTLINES  OF  PHYSICAL  CHEMISTRY 

electrical  energy  obtainable,  n~FE,  and  if  further  the  resistance 
of  the  cell  is  zero  (in  practice,  very  low)  no  heat  will  be  de- 
veloped in  the  calorimeter,  and  the  equivalent  of  Q  calories 
of  electrical  energy  will  pass  round  the  external  wire. 

(b)  If  the  heat  of  reaction  is  greater  than  the  maximum 
electrical  energy  obtainable,  heat  will  be  developed   in   the 
calorimeter  as  well  as  in  the  external  circuit. 

(c)  If  the  heat  of  reaction  is  less  than  the  maximum  electrical 
energy  heat  will  be  absorbed  in  the  calorimeter,  and  the  heat 
equivalent  of  the  electrical  energy  in  the  outer  circuit  will  be 
greater  than   Q  (provided  that  the  resistance  of  the  cell  is 
negligible). 

It  has  already  been  pointed  out  that  the  maximum  work  can 
only  be  obtained  by  carrying  out  a  process  reversibly,  and 
therefore  the  Helmholtz  formula  only  applies  to  elements  in 
which  the  process  can  be  effected  reversibly.  This  means  that 
if  an  element  such  as  the  Daniell  is  giving  out  electrical  energy 
at  an  E.M.F.  represented  by  E,  it  can  be  restored  to  its  initial 
condition  by  passing  through  it,  at  an  E.M.F.  only  just  exceeding 
E,  a  quantity  of  electrical  energy  equal  to  that  given  out.  In 
order  that  an  electrochemical  process  should  be  completely 
reversible,  the  energy  should  be  given  out  and  taken  in  at  the 
same  potential,  which  in  practice  is  impossible.  A  completely 
reversible  process  is  therefore  only  an  ideal  case,  which  can  be 
more  or  less  completely  attained  to  in  actual  practice. 

Many  electrochemical  processes  are  irreversible,  more  par- 
ticularly those  in  which  gases  are  evolved.  For  example,  a 
Daniell  cell  in  which  the  copper  sulphate  solution  is  replaced 
by  sulphuric  acid  is  irreversible,  as,  owing  to  the  escape  of 
hydrogen,  it  cannot  be  restored  to  its  former  condition  by 
passing  a  current  in  the  contrary  direction. 

Measurement  of  Electromotive  Force — The  difference 
of  potential  between  the  two  poles  of  a  cell  may  have  very 
different  values  according  to  the  conditions  of  measurement. 
If  the  poles  are  connected  by  a  wire  of  very  high  resistance, 


ELECTROMOTIVE  FORCE  355 

R,  and  the  resistance  of  the  cell  is  r,  the  fall  of  potential  in 
the  wire  is  CR  and  in  the  cell  Cr.  Since  E  =  C(R  +  r),  it  is 
clear  that  the  fall  of  potential  CR  in  the  outer  circuit  is  only 
equal  to  E  when  the  resistance  R  is  infinitely  large  compared 
with  r.  It  is  therefore  easy  to  understand  why  the  resistance 
of  volt-meters  (instruments  on  which  the  difference  of  potential 
between  two  points  can  be  read  off  directly  in  volts)  is  always 
very  high.  A  further  complication  in  measuring  the  E.M.F. 
of  a  cell  while  working  is  that  in  many  cases  the  products  of 
electrolysis  accumulate  on  the  electrodes,  and  set  up  an  electro- 
motive force  in  the  opposite  direction  to  the  E.M.F.  of  the  cell 
itself — a  phenomenon  which  is  termed  polarization. 

These  difficulties  are  avoided  by  measuring  the  difference  of 
potential  between  the  poles  of  a  cell  when  the  circuit  is  open, 
that  is,  when  the  cell  is  not  sending  a  current.  In  the  present 
chapter,  the  symbol  E  stands  for  the  E.M.F.  of  the  cell  on  open 
circuit.  The  effect  of  completing  the  circuit  will  be  dealt  with 
more  fully  at  a  later  stage. 

The  E.M.F.  of  a  cell  on  open  circuit  is  most  conveniently 
measured  by  the  Poggendorff  compensation  method.  The 
principle  of  the  method  is  that  the  E.M.F.  of  the  cell  is  just 
compensated  by  an  equal  and  opposite  E.M.F.  so  that  no  current 
passes,  and  the  measurement  consists  in  altering  an  adjustable 
E.M.F.  till  the  above  condition  is  fulfilled.  The  arrangement 
of  the  apparatus  for  this  purpose  is  shown  in  Fig.  37.  A  is  a 
lead  accumulator,  or  other  source  of  constant  E.M.F.,  which  is 
connected  to  the  two  ends  of  a  uniform  wire  BC,  which  may 
conveniently  be  a  metre  in  length.  The  cell  E,  the  E.M.F.  of 
which  is  to  be  measured,  is  connected  through  a  sensitive  gal- 
vanometer G  and  a  tapping  key  to  one  end  of  the  bridge  wire 
at  B,  and  on  the  other  to  a  sliding  contact.  The  slider  is  moved 
along  the  wire  until  a  position  D  is  found  at  which,  when  con- 
tact is  made,  no  current  passes  through  the  galvanometer.  It 
is  then  clear  that  the  following  relation  holds  (cf.  p.  255) :  E.M.F. 
of  accumulator :  E.M.F.  of  cell : :  length  BC :  length  BD,  so  that 


356       OUTLINES  OF  PHYSICAL  CHEMISTRY 

the  E.M.F.  of  the  cell  can  readily  be  calculated.  As  the  E.M.F. 
of  the  lead  accumulator  is  not  quite  constant,  it  is  preferable 
in  accurate  determinations  to  standardize  the  apparatus  by  finding 
the  position  on  the  bridge  wire  corresponding  with  the  E.M.F. 
of  a  constant  cell,  such  as  the  Clark  or  Cadmium  cell  (p.  357), 
when  the  latter  is  substituted  for  the  cell  E  in  the  diagram.  As 
null  instrument,  for  showing  that  the  point  of  balance  has  been 
reached,  by  the  fact  that  a  current  no  longer  passes  when 
contact  is  made,  a  high  resistance  galvanometer  or  a  capillary 
electrometer  (p.  378)  may  be  used;  the  former  maybe  made 
the  more  sensitive,  but  the  latter  is  in  many  respects  very 
convenient. 


FIG.  37. 

The  measurement  of  the  E.M.F.  of  a  cell  on  open  circuit 
may  also  be  made  by  means  of  the  quadrant  electrometer,  the 
deflection  of  the  needle  being  proportional  to  E,  but  this  method 
is  in  some  respects  less  advantageous  than  the  compensation 
method. 

In  general,  the  observed  E.M.F.  of  a  cell  on  closed  circuit  is  less 
than  that  on  open  circuit;  this  is  due,  as  already  indicated,  to 
polarization  effects  and  to  the  effect  of  the  internal  resistance 
of  the  cell. 

Standard  of  Electromotive  Force.  The  Cadmium 
Element — The  importance  of  obtaining  a  cell,  the  E.M.F. 
of  which  is  accurately  known,  has  already  been  pointed  out. 


ELECTROMOTIVE  FORCE  357 

The  cadmium  element,  sometimes  called  the  Weston  element,1 
which  is  most  largely  in  use  for  this  purpose,  will  now  be 
described. 

The  cell  itself  consists  of  an  H-shaped  glass  vessel,  the  side 
tubes  are  closed  at  their  lower  ends,  and  platinum  wires,  sealed 
in  the  glass,  pass  through  near  the  lowest  points  of  the  side 
tubes.  In  the  bottom  of  one  of  the  tubes  is  a  layer  of  mercury 
about  i  cm.  deep,  above  which  is  a  paste  (5  mm.)  of  mercurous 
sulphate,  which  has  been  carefully  freed  from  traces  of  mercuric 
salt.  In  the  bottom  of  the  other  side  tube  is  a  layer  of 
cadmium  amalgam  (about  13  per  cent,  of  cadmium  quite  free 
from  zinc)  above  which  is  a  paste  (5  mm.)  of  cadmium  sulphate, 
prepared  by  rubbing  together  in  a  mortar  water  and  crystallized 
cadmium  sulphate,  and  pouring  off  the  clear  saturated  solution. 
The  remainder  of  the  cell  on  both  sides,  as  well  as  the 
connecting  tube,  contains  a  saturated  solution  of  cadmium 
sulphate,  in  which  are  moderately  large  crystals  of  the  solid 
salt,  and  both  side  tubes  are  hermetically  closed  at  the  top, 
a  small  air  space  being  left  to  allow  of  expansion.  When 
required  as  a  standard  of  E.M.F.,  connection  is  made  by  means 
of  the  platinum  wires,  which  are  in  contact  with  the  mercury 
and  amalgam  respectively. 

The  great  advantage  of  the  cadmium  element  is  that  its 
E.M.F.  is  practically  independent  of  temperature.  The  E.M.F. 
at  temperatures  from  o°  to  30°  is  as  follows  : — 

o°  5°  10°          15°         20°          25°         30° 

1-0189    1-0189    1*0189    1*0188    roi86    1*0184   1-0181  volts, 

the  mercury  being  positive. 

When  in  use  the  element  should  only  be  allowed  to  send  a 
very  small  current  for  a  very  short  time;  if  this  condition  is 
not  observed  the  E.M.F.  soon  alters  owing  to  polarization. 

The  mode  of  action  of  the  element  will  be  understood  when 
the  section  on  the  calomel  electrode  has  been  read. 

1  The  true  Weston  element  differs  slightly  from  that  here  described. 


358       OUTLINES  OF  PHYSICAL  CHEMISTRY 

The  corresponding  cell  with  zinc  amalgam  and  zinc  sulphate 
instead  of  cadmium  amalgam  and  cadmium  sulphate,  was 
formerly  in  general  use  as  a  standard  element  under  the  name 
of  the  Clark  cell.  Its  chief  drawback  is  that  the  E.M.F.  alters 
considerably  with  temperature.  The  E.M.F.  of  the  Clark  cell 
is  given  by  the  equation 

E  =  1*4328  -  o'ooiig  (/  —  15°)  -  o'oooooy  (t  —  i5)2. 

Solution  Pressure — In  a  former  section  it  has  been  shown 
that  the  relation  between  chemical  and  electrical  energy  in-  a 
voltaic  cell  is  given  by  the  Helmholtz  formula 

F        Q  4.  T  d£ 
E  =  »F  +  TJf 

This  formula  has  been  deduced  from  considerations  which  are 
quite  independent  of  any  assumption  as  to  the  mechanism  of 
the  establishment  of  differences  of  potential  in  a  cell,  and 
therefore  holds  quite  independently  of  any  theory  as  to  the 
origin  of  differences  of  potential.  A  much  deeper  insight  into 
this  problem  is  gained  on  the  basis  of  a  theory  due  to  Nernst, 
based  on  the  theory  of  electrolytic  dissociation,  and  this  theory 
will  now  be  considered. 

Every  substance  has  a  tendency  to  change  from  the  form  in 
which  it  actually  exists  to  another  form.  Water,  for  example, 
has  a  tendency  to  pass  into  vapour,  and  if  the  vapour  be  con- 
tinually removed  from  its  surface,  a  definite  quantity  of  water 
will  change  completely  to  vapour.  The  tendency  in  question 
is  measured  by  the  vapour  pressure  of  the  water,  and  is  con- 
stant at  constant  temperature.  Further,  a  solid,  such  as  sugar, 
when  brought  in  contact  with  water,  tends  to  pass  into  solution, 
and  from  the  analogy  with  water  and  water  vapour  we  may  say 
that  sugar  has  a  definite  solution  pressure,  which  is  constant  at 
constant  temperature,  since  the  active  mass  of  a  solid,  such  as 
sugar,  is  constant  (p.  173).  On  the  other  hand,  the  dissolved 
sugar  has  a  tendency  to  separate  in  the  solid  form,  which  is  the 
greater  the  higher  the  concentration,  and  when  the  solution  is 


ELECTROMOTIVE  FORCE  359 

supersaturated  the  tendency  to  the  separation  of  solid  sugar  is 
greater  than  the  tendency  of  the  latter  to  pass  into  solution. 
From  the  considerations  advanced  on  p.  98,  it  is  clear  that 
the  pressure  of  the  sugar  in  solution  is  its  osmotic  pressure,  and 
under  definite  conditions  sugar  will  enter  into  or  separate  from 
solution  according  as  its  solution  pressure  is  greater  or  less  than 
its  osmotic  pressure. 

These  considerations,  in  conjunction  with  the  ionic  theory, 
enable  us  to  express  the  E.M.F.  at  a  junction  metal/solution 
in  terms  of  solution  pressure  and  osmotic  pressure.  If  a  metal 
is  dipped  into  water  it  tends  to  dissolve,  in  consequence  of  its 
solution  pressure,  P,  and  as  it  can  only  do  so  in  the  ionic  form, 
it  sends  a  certain  number  of  positive  ions  into  solution.  The 
solution  thus  becomes  positively  charged,  and  the  metal,  which 
was  previously  neutral,  becomes  negatively  charged  in  conse- 
quence of  the  loss  of  positive  ions.  This  process  will  proceed 
until,  by  the  accumulation  of  positive  electricity  in  the  solution, 
the  latter  becomes  so  strongly  positive  that  it  prevents  the  pas- 
sage of  more  positive  ions  into  solution.  As  the  charge  on 
the  ions  is  so  great,  this  process  comes  to  a  standstill  when  the 
amount  of  ions  gone  into  solution  is  still  excessively  small,  too 
small  to  be  detected  by  analytical  means. 

The  state  of  affairs  is  rather  different  when  a  metal  is  dipped 
into  a  solution  of  one  of  its  salts,  e.g.,  zinc  in  a  solution  of  zinc 
sulphate.  In  this  case  there  are  already  positive  metallic  ions 
in  the  solution,  which  tend  to  resist  the  entrance  of  further 
positive  ions,  and  what  actually  occurs  will  clearly  depend  upon 
the  relative  values  of  the  solution  pressure,  P,  of  the  metal  and  the 
osmotic  pressure,  p,  of  the  ions  in  solution.  There  are,  in  fact, 
three  possible  cases,  which  are  represented  diagrammatically  in 
the  accompanying  figure  : — 

(a)  If  P  >  p,  the  metal  sends  ions  into  the  solution  until  the 
accumulated  electrostatic  charges  prevent  further  action ;  the 
metal  is  then  negatively  and  the  solution  positively  charged. 

(b]  If  P  <  py  the  positive  ions  from  the  solution  deposit  on 


360       OUTLINES  OF  PHYSICAL  CHEMISTRY 


the  metal  until  the  electrostatic  charges  prevent  further  action  ; 
the  metal  is  then  positively  and  the  solution  negatively  charged. 

(c)  If  P  =  /,  no  change  occurs,  and  there  is  no  difference  of 
potential  between  metal  and  solution. 

As  will  be  shown  later,  the  solution  pressures  of  the  different 
metals  are  very  different.  Those  of  the  alkali  metals,  zinc,  iron, 
etc.,  are  so  great  that  they  always  exceed  the  osmotic  pressures 
of  their  respective  solutions  (which  cannot  be  increased  beyond 
a  certain  point  owing  to  the  limited  solubility  of  the  salts),  and 
these  metals  are,  therefore,  always  negatively  charged  with 


- 

Metal 

, 

- 

-1- 

+  Solution. 

Metal 

Solution. 

\ 

Metal 

- 

- 

.  Solution. 

p-p. 

FIG.  38. 


P<p. 


reference  to  their  solutions.  On  the  other  hand,  the  solution 
pressure  of  mercury,  silver,  copper,  etc.,  is  so  small  that  they 
become  positively  charged,  even  in  very  dilute  solutions  of  their 
respective  salts. 

Calculation  of  Electromotive  Forces  at  a  Junction 
Metal/Salt  Solution — Provided  that  the  changes  at  the 
junction  of  an  electrode  with  a  solution  are  reversible,  the 
E.M.F.  at  the  junction  can  readily  be  calculated  in  terms  of 
the  solution  pressure,  P,  of  the  metal  and  the  osmotic  pressure, 
p,  of  the  solution.  This  can  perhaps  be  done  most  simply  by 
calculating  the  maximum  work  obtainable  when  a  mol  of 


ELECTROMOTIVE  FORCE  361 

the  electrode  metal  is  brought  from  the  pressure  P  to  the  lower 
pressure  /,  (i)  osmotically,  (2)  electrically.  If  a  mol  of  a 
dissolved  substance  is  brought  reversibly  from  the  pressure  P 
to  p  the  work  gained  (in  this  case  the  osmotic  work)  is  (cf.  p. 
135) 


Further,  the  dissolving  of  i  equivalent  of  a  metal  is  associated 
with  96,540  coulombs,  and  that  of  a  mol  of  a  metal  of  valency 
n  with  96,540  n  coulombs.  The  work  done  is  the  product  of 
the  E.M.F.  E  in  volts  and  the  quantity  of  electricity,  96,540  n 
coulombs.  Equating  the  osmotic  and  electrical  work,  we  have 
n  96,540  E  =  RTlog.P// 

RT      .      P  t\ 

or  E  =  —  -  log*-  •         •         (i) 

96,540;*      &  p 

In  order  to  obtain  E  in  volts,  R  must  be  expressed  in  electrical 
units  (volt-coulombs).  If,  at  the  same  time,  the  change  is  made 
to  ordinary  logarithms  (by  multiplying  by  2  '3  02  6)  the  above 
equation  becomes 

2-3026  x   1-99  x  4-183  T         P     0-0001983  T         P 

96,540.          loglo/=     —     logl<7 

The  numerical  values  of  2*3026  RT/Fat  o°,  18°,  25°  and  30° 
are  as  follows  :  — 

Absolute  temperature  273°  273  +  18°  273  +  25°  273  +  30  . 
Value  of  2*3026  RT/F  0*0541  0*0577  0*0591  0*0601 

At  room  temperature  (15-20°)  the  value  of  the  expression  in 
question  is  about  0*058,  and  the  general  formula  becomes 

;   B-  2255*0^    -       -       .       („ 

which  should  be  remembered.  It  is  clear  from  the  form  of 
the  above  equation  that  a  tenfold  increase  or  decrease  in  the 
osmotic  pressure  of  the  ions  of  the  metal  will  produce  a  change 
of  E.M.F.  of  0*058  volts  for  a  univalent  metal,  and  0*058/72 
volts  for  a  ^-valent  metal,  at  room  temperature. 


362        OUTLINES  OF  PHYSICAL  CHEMISTRY 


Differences  of  Potential  in  a  Voltaic  Cell— Two  such 
electrodes  as  have  just  been  described  may  be  combined 
together  to  form  a  voltaic  cell.  This  may  be  done  in  many 
ways,  but  a  convenient  arrangement  is  that  for  the  Daniell 
cell  represented  in  Fig.  39.  in  which  the  solutions  are  separated 
by  a  porous  partition,  A,  which  prevents  convection,  but  allows 
the  current  to  pass.  When  the  poles  are  placed  in  the  respec- 
tive solutions,  the  zinc  becomes  negatively  charged,  since  Pj> 
pl  ;  on  the  other  hand,  the  copper  becomes  positively  charged 
as/2>P2.  As  already  explained,  the  solution  and  precipita- 
tion soon  come  to  a  standstill  because  of  the  accumulation 

of  electrostatic  charges. 


Zh 


Cu 


Cu-SO, 


FIG.  39. 


If,  however,  the  elec- 
trodes are  connected 
by  a  wire,  the  contrary 
charges  neutralize  each 
other  through  the  wire, 
and  in  the  solution 
more  metal  can  then 
be  dissolved  and  de- 
posited respectively  (as 
there  are  no  longer  any 
opposing  forces),  the 
corresponding  charges  are  again  neutralized,  and  so  on.  The 
neutralization  of  charges  through  a  conductor  corresponds  with 
the  passage  of  a  current. 

The  general  question  as  to  the  seat  of  the  E.M.F.  in  such 
a  cell  as  the  Daniell  has  now  to  be  considered.  If  the  poles 
of  the  cell  are  connected  by  a  wire  of  metal  M,  there  are  no  less 
than  five  junctions  at  which  there  may  be  contact  differences  of 
potential ;  two  metallic  junctions,  Zn/M  and  M/Cu,  two  metal/ 
solution  junctions,  Cu/CuSO4  and  Zn/ZnSO4,  and  one  liquid 
junction,  ZnSO4/CuSO4.  The  question  as  to  whether  there 
are  contact  differences  of  potential  at  the  junction  of  two  metals 
gave  rise  to  great  difference  of  opinion,  and  the  controversy 


ELECTROMOTIVE  FORCE 


363 


lasted  the  greater  part  of  last  century.  It  is  now  generally 
agreed,  however,  that  if  there  are  such  differences  they  are 
exceedingly  small  in  comparison  with  those  of  the  junctions 
metal/salt  solution.  The  difference  of  potential  at  the  liquid 
junction  is  of  much  more  importance  and  can  be  calculated  by 
Nernst's  theory  (p.  384).  It  also  is  small  in  comparison  with 
those  at  the  liquid/metal  junctions,  and  may,  therefore,  be  left 
out  of  account  for  the  present. 

The  distribution  of  differences  of  potential  in  the  Daniell  cell 
with  open  circuit  is  represented  in  Fig.  40  (a),  the  ordinates 


(„ 


FIG.  40. 


representing  the  potentials  of  the  different  parts  of  the  circuit. 
The  horizontal  lines,  AB,  CD,  DE  and  FG,  illustrate  the  very 
important  fact  that  the  copper,  the  zinc  and  the  solutions  are 
each  of  a  definite  constant  potential,  and  the  ordinates,  BC  and 
EF,  that  there  are  sudden  alterations  of  potential  at  the  junc- 
tions metal/solution.  For  simplicity  the  solutions  of  zinc 
sulphate  and  copper  sulphate  are  represented  as  being  at  the 
same  potential,  which  is  only  approximately  true.  It  is  as- 
sumed for  the  present  that  the  difference  of  potential  be- 
tween copper  and  N  copper  sulphate  solution  is  0*585  volts, 
the  copper  being  positive,  and  that  the  potential  difference, 
Zn/«ZnSO4,  is  0*52  volts,  the  metal  being  negative.  The 


364        OUTLINES  OF  PHYSICAL  CHEMISTRY 

total  difference  of  potential  between  zinc  and  copper  on  open 
circuit  is  thus  0-585  +  0-52  =  1-105  volts. 

When  the  circuit  is  closed  by  connecting  the  copper  and  zinc 
by  a  wire  of  fairly  high  resistance,  R,  the  distribution  of  poten- 
tial in  the  cell  is  as  shown  in  Fig.  40  (d).  The  sudden  changes 
of  potential  at  the  junctions  ZnSO4/Zn  and  CuSO4/Cu  are 
of  the  same  magnitude  as  before,  but  the  difference  of  potential 
between  the  zinc  and  copper,  measured  by  the  vertical  height, 
AG,  is  much  less  than  on  open  circuit.  This  is  owing  to  the 
fall  of  potential  in  the  cell  owing  to  the  resistance  of  the  elec- 
trolyte, so  that  the  solution  in  contact  with  the  zinc  is  at  a 
higher  potential  than  that  in  contact  with  the  copper,  as  repre- 
sented by  EDC.  If  C  is  the  current  passing  through  the  cell, 
and  r  is  the  resistance  of  the  electrolyte,  the  E.M.F.  of  the  cell 
on  closed  circuit  is  given  by  E  =  CR  +  Cr,  and  CR,  the  fall  of 
potential  in  the  external  wire  (represented  in  the  figure  by  the 
vertical  distance  AG),  approaches  the  more  nearly  to  the  E.M.F. 
of  the  same  cell  on  open  circuit  the  greater  R  is  compared  with 
r  (compare  p.  355). 

The  E.M.F.  of  such  a  combination  as  the  Daniell  cell  is  the 
algebraic  sum  of  the  E.M.F.s  at  the  two  junctions,  and  is 
represented  by  the  formula 


Where  P1  and  P2  are  the  solution  pressures  of  zinc  and  copper 
respectively,  ^  represents  the  osmotic  pressure  of  the  zinc  ions 
in  the  solution,  and  /2  that  of  the  copper  ions.  The  values  of 
pl  and  /2  are  therefore  known,  but  the  absolute  values  of  the 
solution  pressures  Pj  and  P2  are  unknown.  The  -  sign  of 
E2  is  due  to  the  fact  that  at  that  junction  ions  are  leaving  the 
solution. 

In  obtaining  E  as  the  algebraic  sum  of  the  differences  of 
potential  ET  and  E2  at  the  two  junctions,  it  is  naturally  of  the 
utmost  importance  to  take  the  values  of  Ej  and  E2  with  their 
proper  sign.  Perhaps  the  best  method  of  avoiding  errors  in  this 


ELECTROMOTIVE  FORCE  365 

connection  is  to  consider  the  tendency  of  one  kind  of  electricity, 
say  positive  electricity,   to  pass  round  the  circuit.     In  going 
round  the   circuit  in  the  Daniell  cell,  starting  with  the  zinc, 
the  different  junctions  are  met  with  in  the  order 
Zn  |  ZnSO4  |  CuSO4  |  Cu 

0-52  °'5&5 


1*105 

and  this  is  a  very  convenient  method  of  representing  the  Daniell 
or  any  other  cell. 

Now  at  the  junction  Zn/ZnSO4  positive  electricity  tends  to 
pass  from  zinc  to  solution  at  a  potential  (pressure)  of  0*52 
volts,  as  indicated  by  the  arrow.  Further,  as  the  osmotic  pres- 
sure of  Cu"  ions  in  copper  sulphate  solution  is  greater  than  the 
solution  pressure  of  copper,  positive  electricity  tends  to  pass 
across  the  junction  CuSO4/Cu,  in  the  direction  of  the  arrow  at 
an  E.M.F.  of  0-585  volts.  It  is  clear  that  the  forces  at  the 
two  poles  are  in  the  same  direction,  and  therefore  positive 
electricity  tends  to  pass  through  the  solution  in  the  direction 
indicated  by  the  lower  arrow  at  a  total  E.M.F.  of 

0-520  +  0-585  =  1-105  volts. 
Further  illustrations  are  given  at  a  later  stage. 

Influence  of  Change  of  Concentration  of  Salt  Solution 
on  the  E.M.F.  of  a  Cell  —  The  general  equation  just  given 
may  be  written  in  a  slightly  different  form  by  substituting  for 
the  pressures  the  corresponding  concentrations.  Considering 
first  the  solution  pressure,  Plt  of  the  zinc,  it  is  theoretically 
possible  to  choose  a  Zn"  ion  concentration,  Clt  such  that  its 
osmotic  pressure  will  just  balance  the  solution  pressure  of  the 
metal  ;  this  may  be  substituted  for  P1  in  the  general  equation. 
Similarly,  for  /»1?  the  osmotic  pressure  of  the  zinc  ions  in  the 
solution,  we  may  substitute  the  corresponding  concentration, 
cr  Dealing  in  the  same  way  with  the  copper  side  of  the  cell, 
the  equation  for  the  Daniell  cell  (or  any  other  cell  of  similar 
type)  becomes 


366        OUTLINES  OF  PHYSICAL  CHEMISTRY 


In  this  form  the  general  equation  may  be  employed  to  in- 
vestigate the  question  as  to  how  the  E.M.F.  of  the  cell  is 
affected  by  varying  the  concentration  of  the  salt  solutions. 
For  the  zinc  side,  since  Cj  is  greater  than  clt  it  is  clear  that 
the  quotient  CJclt  and  therefore  Elf  is  increased  by  diminish- 
ing clt  the  concentration  of  the  Zn"  ions.  For  the  copper 
side,  however,  as  C2  is  less  than  c2  (p.  342),  the  quotient 
C2Ar2,  therefore  E2,  will  evidently  be  diminished  by  diminishing 
the  copper  sulphate  concentration.  The  general  rule  with  re- 
gard to  the  influence  of  change  of  ionic  concentration  on  the 
E.M.F.  of  a  cell  may  be  expressed  as  follows  :  Diminishing  the 
concentration  of  a  solution  from  which  ions  are  separating  lowers, 
and  diminishing  the  concentration  of  a  solution  into  which  new 
ions  are  going  increases,  the  E.M.F.  of  a  cell.  It  is  evident 
from  general  principles  that  the  effect  must  be  as  described  ; 
in  the  first  case,  the  tendency  to  the  separation  of  ions  is 
lessened,  and  the  E.M.F.  falls  ;  in  the  second  case,  the 
entrance  of  new  ions  is  facilitated,  and  the  E.M.F.  increases. 

If  the  concentration  of  the  Cu"  ions  in  the  solution  is  pro- 
gressively diminished,  a  point  must  be  reached  at  which  the 
solution  pressure  'of  the  metal  is  just  balanced  by  the  osmotic 
pressure  of  the  Cu"  ions.  If  the  concentration  is  still  further 
diminished,  the  tendency  for  copper  to  pass  into  solution  will 
steadily  increase,  and  ultimately  may  become  greater  than  the 
tendency  of  zinc  to  pass  into  solution.  It  should  therefore  be 
theoretically  possible  to  reverse  the  direction  of  the  current  in 
the  Daniell  cell  by  sufficiently  diminishing  the  Cu"  ion  con- 
centration, and  this  state  of  affairs  can  be  realised  experimentally 
by  adding  potassium  cyanide  to  the  copper  sulphate  solution. 

A  further  important  deduction  can  also  be  drawn  from  the 
general  equation.  As  c±  and  <r2  stand  for  the  concentration 
of  the  positive  ions  in  the  solution,  the  E.M.F.  of  the  cell 
should  be  independent  of  the  nature  of  the  negative  ion,  pro- 


ELECTROMOTIVE  FORCE  367 

vided  that  the  salts  are  equally  ionised.  This  consequence  of 
the  theory  is  completely  borne  out  by  experiment.  For  twenty- 
one  different  thallium  salts,  in  N/5o  solution,  the  difference  of 
potential  between  metal  and  solution  varied  only  from  07040 
to  0*7055  volts,  the  slight  variations  being  reatiily  accounted 
for  by  differences  in  the  degree  of  ionisation. 

Concentration  Cells — We  have  now  to  consider  what  are 
termed  "concentration  cells,"  cells  in  which  the  E.M.F.  de- 
pends essentially  on  differences  of  concentration.  In  some 
respects,  concentration  cells  are  simpler  than  those  of  the 
Daniell  type,  which  have  so  far  been  considered. 

Concentration  cells  may  be  divided  into  two  main  classes — 

(a)  Those  in  which  the  solutions  are  of  different  concen- 

trations. 

(b)  Those  in  which  the  substances  yielding  the  ions  are  of 

different  concentrations. 

(a)  Concentration  Cells  with  Solutions  of  Different  Concen- 
trations— As  a  type  of  the  elements  in  question,  we  will  con- 
sider a  cell  in  which  silver  electrodes  dip  in  solutions  of  silver 
nitrate  of  different  concentrations,  ^  and  c%.  The  arrange- 
ment for  the  practical  determination  of  the  total  E.M.F.  of 
such  a  combination  is  shown  in  Fig.  41,  where  A  and  B  repre- 
sent the  cells  containing  the  silver  nitrate  solutions  and  the 
vessel  C  contains  an  indifferent  electrolyte.  As  this  form  of 
cell  is  largely  employed  in  measurements  of  E.M.F.,  it  may  be 
well  to  describe  it  fully.  It  consists  of  a  glass  tube  3-4  cm. 
wide,  with  a  straight  side-tube  D  on  one  side  and  a  bent  side- 
tube  E  on  the  other,  the  latter  being  employed  for  making  con- 
nection with  the  indifferent  electrolyte  in  C  as  shown.  Into  the 
lower  end  of  a  glass  tube,  F,  is  cemented  a  thick  rod  of  silver 
covered  with  the  finely-divided  metal  by  electrolysis,  and  the 
glass  tube  is  held  by  a  cork  closing  the  cell.  The  cell  is  filled 
with  a  solution  of  silver  nitrate  of  definite  strength  through  the 
bent  tube  by  suction  through  the  straight  side-tube,  D,  which 
is  then  closed  by  a  clip.  The  other  "  half-cell,"  B,  is  prepared 


368       OUTLINES  OF  PHYSICAL  CHEMISTRY 


in  exactly  the  same  way,  but  contains  a  solution  of  silver  nitrate 
of  different  concentration.  The  ends  of  the  bent  tubes  are 
then  dipped  into  an  indifferent  electrolyte  in  the  vessel,  C,  as 
shown,  and  the  total  E.M.F.  of  the  combination  determined  by 
the  potentiometer  method  in  the  usual  way,  connection  with 
the  silver  electrodes  being  made  by  wires  passing  down  the 
interior  of  the  glass  tubes.  In  this  case,  the  general  equation 
for  an  electrolytic  cell, 


C 

—  -    logio 


C9\ 

-M 
c^J 


simplifies  to 


— 
E 


(i) 


FIG.  41. 

since  C,  the  solution  pressure  of  the  metal,  is  the  same  on  both 
sides,  and  is  therefore  eliminated.     A  cell  of  the  type 

Ag  I  AgNO3dil     AgNO3conc     Ag 


works  in  such  a  way  that  silver  is  deposited  from  the  more 
concentrated  solution,  in  which  the  osmotic  pressure  is  higher, 
and  is  dissolved  at  the  pole  in  contact  with  the  weaker  solution, 
which  offers  less  resistance  to  the  entrance  of  Ag'  ions.  The 


ELECTROMOTIVE  FORCE  369 

change,  therefore,  proceeds  in  such  a  way  that  the  differences 
of  concentration  tend  to  equalize,  and  when  the  solutions  have 
reached  the  same  concentration,  the  current  stops.  Positive 
electricity  therefore  passes  in  the  element  from  the  weak  to  the 
strong  solution,  as  indicated  by  the  arrow,  and  in  the  connecting 
wire  from  the  strong  to  the  weak  solution ;  the  electrode  in 
contact  with  the  strong  solution  becomes  positively  charged, 
the  other  electrode  negatively  charged. 

The  equation  shows  that  the  E.M.F.  of  such  a  concentra- 
tion cell  depends  only  on  the  respective  concentrations  of  the 
positive  ions  in  the  two  solutions  and  their  valency,  and  not  on 
the  nature  of  the  electrodes  or  on  the  nature  of  the  anions,  and 
the  experimental  results  are  in  full  accord  with  this  deduction. 
Otherwise  expressed,  the  E.M.F.  of  any  element  made  up  of  a 
univalent  metal  M  dipping  in  solutions  of  one  of  its  salts  of 
different  concentration  is  of  the  same  absolute  value  as  that  of 
the  silver  concentration  cell,  provided  that  the  solutions  are 
of  corresponding  concentration,  and  ionised  to  the  same  extent. 
Further,  if  the  solutions  are  dilute,  and  electrolytic  dissociation 
therefore  fairly  complete,  the  ratio  of  the  ionic  concentrations  in 
different  dilutions  will  be  approximately  the  same  as  the  ratio  of 
the  concentrations  themselves.  Thus,  in  the  example  under 
consideration,  the  ratio  cjc-^  for  i/ioo  molar,  and  i/iooo  molar 
solutions,  will  be  approximately  10  :  i ;  Iog10f2/f1  is  therefore  i, 
and  the  value  of  E  for  the  cell 


Ag  |  AgN03   |  AgNO< 

I  m/iooo   \  m/ioo 


Ag 


is  o'o$S/n  =  0*058  volts,  since  n,  the  valency  of  the  ions  con- 
cerned, is  unity. 

If,  however,  the  solutions  are  more  concentrated,  the  fact 
that  ionisation  is  incomplete  must  be  taken  into  account  in 
calculating  the  E.M.F.  of  a  cell.  Suppose,  for  instance,  it  is 
required  to  calculate  the  E.M.F.  of  the  cell 

Ag  |  AgNO3  m/ 100  \  AgNO3  m/io\  Ag. 
24 


370       OUTLINES  OF  PHYSICAL  CHEMISTRY 

N/io  silver  nitrate  solution  is  ionised  to  the  extent  of  82 
per  cent,  at  18°,  whence  c%  =  0-082,  and  N/ioo  silver  nitrate 
to  the  extent  of  94  per  cent.,  whence  ^  =  0-0094.  We  have 
therefore  cjc^  —  o'o82/o'oo94  =  8*72,  and  E  =  0*054  volts,  in 
excellent  agreement  with  the  experimental  value. 

Strictly  speaking,  it  is  not  justifiable  in  cells  of  this  type  to 
neglect  the  contact  difference  of  potential  between  the  two 
solutions,  which  may  amount  to  a  considerable  fraction  of  the 
total  E.M.F.  The  accurate  formula  for  the  calculation  of  the 
E.M.F.  of  cells  of  this  type  is  given  in  a  succeeding  section  (p. 
384).  If,  however,  both  solutions  contain  an  indifferent  electro- 
lyte in  equivalent  concentration  great  in  comparison  with  those 
of  the  active  salt,  the  difference  of  potential  at  the  liquid 
junction  becomes  negligible,  and  the  above  formula  (i)  holds 
accurately  (cf.  p.  383). 

It  is  evident  from  the  formula  that  the  E.M.F.  of  a  con- 
centration cell  cannot  be  greatly  increased  by  increasing  the 
concentration  on  one  side,  owing  to  the  limited  solubility  of 
the  salts  used  as  electrolytes.  On  the  other  hand,  the  E.M.F. 
may  be  greatly  increased  by  diminishing  the  ionic  concentra- 
tion on  one  side.  Conversely,  when  a  cell  is  made  up  with 
a  solution  of  silver  nitrate  of  known  Ag'  ion  concentration,  clt 
and  one  of  unknown  concentration,  c0t  and  the  E.M.F.  of  the 
cell  is  measured,  c0  can  readily  be  calculated.  This  principle 
has  been  applied  more  particularly  for  the  determination  of 
very  small  ion  concentrations,  and  may  be  illustrated  by  the 
determination  of  the  Ag'  ion  concentration  in  a  saturated 
solution  of  silver  iodide.  When  the  concentration  on  one  side 
is  very  small,  it  is  usual  to  add  some  salt,  with  or  without  a 
common  ion,  to  eliminate  the  potential  difference  at  the  liquid 
junction,  and  also  to  increase  the  conductivity  in  the  cell,  so 
as  to  render  the  measurements  more  accurate.  In  this  case 
potassium  nitrate  may  conveniently  be  used.  The  observed 
E.M.F.  of  the  cell 

Ag  |  KNO3  +  Agl  |  AgNO3  o-ooim  +  KNO3  Ag 


ELECTROMOTIVE  FORCE  371 

is  0*22  volts.     Since  cl  =  o'ooi,  we  have 

E  =  0-22  =  0-058  Iog10(o -oo i/<:0), 

whence  c0  =  i'6  x  io~8.  In  other  words,  a  litre  of  a  saturated 
solution  of  silver  iodide  contains  i'6  x  io~8  mol  of  silver 
iodide,  in  excellent  agreement  with  the  value,  1-5  x  io~8  mol, 
obtained  from  conductivity  measurements  (p.  301). 

(b)  Cells  with  Different  Concentrations  of  the  Elec- 
trode Materials  (Substances  Producing  Ions) — Not  only 
can  concentration  cells  be  obtained  by  employing  different  con- 
centrations of  an  electrolyte,  but  also  by  using  metals,  or  other 
substances  yielding  ions  in  different  concentrations.  The  con- 
centration of  metals  can  for  our  present  purpose  be  most  satis- 
factorily varied  by  employing  their  solutions  in  mercury,  the 
so-called  amalgams.  For  example,  a  concentration  cell  can 
readily  be  built  up  as  follows : — 
Zinc  amalgam  conc./zinc  sulphate  solution/ zinc  amalgam  dilute 


which  differs  from  the  cells  of  the  first  type  in  that  the  osmotic 
pressure  of  the  zinc  ions  in  contact  with  the  two  poles  is  the 
same,  but  the  concentration,  and  therefore  the  solution  pressure 
of  the  metal  on  the  two  sides,  is  different. 

The  E.M.F.  of  a  cell  of  this   type   is  represented  by  the 
general  formula  (p.  361) 

E  = 


Since  the  same  solution  (in  this  case  zinc  sulphate)  is  in  contact 
with  both  electrodes,  p±  =/2,  and  the  formula  becomes 


n  >10P2 

On  the  assumption  that  Px  and  P2,  the  solution  pressure  of  the 
zinc  in  the  concentrated  and  dilute  amalgams  respectively,  are 
proportional  to  the  respective  concentrations,  we  obtain 

„,       o'oooio83T.        CT 
— Iog10^r 

¥1  {^sn 


372       OUTLINES  OF  PHYSICAL  CHEMISTRY 

which  is  exactly  the  same  form  of  equation  as  that  for  cells 
with  different  electrolyte  concentrations. 

As  the  solution  pressure  of  the  zinc  is  higher  in  the  con- 
centrated amalgam,  it  passes  into  solution  from  the  latter  and 
is  deposited  in  the  less  concentrated  amalgam,  so  that  the  con- 
centrations tend  to  become  equal.  It  follows  that  positive 
electricity  passes  in  the  cell  from  the  concentrated  to  the  dilute 
amalgam,  as  shown  by  the  arrow. 

As  an  illustration,  the  E.M.F.  of  a  cell  for  which  Cx  =  0*14 
mol  and  C2  =  0*00214  mol  of  zinc  per  litre  of  amalgam  at  23° 
may  be  calculated.     If  it  be  assumed  that  zinc  is  unimolecular 
when  dissolved  in  mercury,  n  =  2,  and 
T,        0*0001083  x  296 
- 


in  excellent  agreement  with  the  observed  value,  0-052  volts. 

So  far,  the  possible  effect  of  mercury  on  the  potential  has 
been  disregarded,  and  this  is  justified  by  the  excellent  agreement 
between  observed  and  calculated  values  for  the  E.M.F.  on  the 
assumption  that  mercury  simply  acts  as  an  indifferent  solvent. 
The  explanation  is  that  for  a  mixture  of  two  metals  it  is  the 
metal  with  the  higher  solution  pressure  that  goes  into  solution, 
and  mercury  can  consequently  be  used  as  solvent  in  potential 
measurements  for  any  metal  which  is  "less  noble,"  i.e.,  which 
has  a  higher  solution  pressure  than  mercury  itself. 

As  indicated  above,  the  E.M.F.  of  a  metal  dissolved  in  mer- 
cury depends  on  the  concentration.  The  difference  of  potential 
between  a  saturated  solution  of  a  metal  in  mercury  and  an 
aqueous  solution  of  one  of  its  salts  is  the  same  as  that  between 
the  salt  solution  and  the  pure  metal,  and  even  for  dilute  amal- 
gams the  E.M.F.  is  not  very  different  from  that  of  the  pure 
metal,  as  the  example  shows.  On  the  other  hand,  the  potential 
of  a  metal  in  chemical  combination  with  a  more  noble  metal 
may  be  quite  different  from  that  of  the  pure  metal. 

The  energy  relations  in  concentration  cells  in  which  very 
dilute  solutions  are  employed  are  remarkable.  In  the  silver 


ELECTROMOTIVE  FORCE  373 

nitrate  concentration  cell  described  above,  the  change  con- 
sisted simply  in  bringing  Ag  ions  from  the  pressure  /j  to 
the  lower  pressure  /2.  When  a  perfect  gas  expands  from  the 
pressure  pl  to  /2,  no  internal  work  is  done,  and  this  is  the 
more  nearly  the  case  for  ordinary  gases  the  lower  the  pressures. 
In  an  exactly  corresponding  way  no  internal  work  will  be  done 
when  a  salt  is  further  diluted  in  sufficiently  dilute  solution  ;  in 
other  words,  the  heat  of  dilution  will  be  zero.  This  means 
that  the  change  of  chemical  energy  (Q  in  the  Helmholtz 
formula),  also  termed  the  heat  of  reaction,  is  zero,  so  that  the 
electrical  energy  obtained  from  a  concentration  cell  with  suffi- 
ciently dilute  solutions  does  not  come  from  a  chemical  change 
at  all,  but  entirely  from  the  surroundings.  Under  these  circum- 
stances, as  Q  is  zero,  the  Helmholtz  formula  simplifies  to 


F 


Electrodes  of  the  First  and  Second  Kind.  The  Calomel 
Electrode  —  So  far  only  electrodes  which  are  reversible  with 
regard  to  the  positive  ion  have  been  considered;  these  are 
termed  electrodes  of  the  first  kind.  In  an  exactly  similar  way  it 
is  possible  to  construct  electrodes  which  are  reversible  with 
regard  to  the  negative  ion  —  these  are  termed  electrodes  of  the 
second  kind.  The  most  important  electrode  of  the  latter  type 
is  the  calomel  electrode,  which  consists  of  mercury  in  contact 
with  solid  mercurous  chloride  and  a  saturated  solution  of  the 
latter  salt  in  potassium  chloride  solution  as  electrolyte.  The 
calomel  electrode  is  reversible  with  regard  to  Cl'  ions,  just  as 
the  Cu/CuSO4  electrode  is  reversible  with  regard  to  Or*  ions. 
If  positive  electricity  passes  from  metal  to  solution,  the  mercury 
combines  with  Cl'  ions  and  calomel  is  formed  ;  if  passed  in  the 
reverse  direction  chlorine  goes  into  solution  and  solid  calomel 
disappears.  The  electrode,  therefore,  acts  like  a  plate  of 
solid  chlorine,  which  gives  up  or  absorbs  the  element  de- 
pending on  the  direction  of  the  current. 


374       OUTLINES  OF  PHYSICAL  CHEMISTRY 

In  order  more  fully  to  illustrate  the  above  statements  with 
regard  to  the  calomel  electrode,  we  will  consider  the  working  of 
the  "double  concentration  cell" — 

Zn  |  ZnCl2dil  |  HgCl  |  Hg  |  HgCl  |  ZnCl2conc  |  Zn 


obtained  by  interposing  a  calomel  electrode  between  the  half- 
elements  Zn/ZnCL>dil  and  ZnCl2conc/Zn. 

Positive  electricity  passes  in  the  cell  in  the  direction  of  the 
arrow,  zinc  dissolving  in  the  dilute  solution  and  being  deposited 
from  the  concentrated  solution,  so  that  the  net  result  of  the  pro- 
cess is  the  transference  of  zinc  chloride  from  the  concentrated  to 
the  dilute  solution.  The  calomel  electrode,  however,  plays  an 
essential  part  in  the  process.  When  i  mol  of  zinc  dissolves  in 
the  dilute  solution,  two  equivalents  of  mercury  are  liberated 
from  the  calomel  and  two  equivalents  of  Cl'  ions  remain  in 
solution.  At  the  other  side  of  the  compound  cell,  a  mol  of 
zinc  is  deposited,  and  simultaneously  two  equivalents  of  mercury 
combine  with  the  equivalent  amount  of  chlorine  to  form  calomel. 
The  calomel  electrode  has  therefore  been  instrumental  in  effect- 
ing the  transference  of  the  Cl'  ions,  and  has  acted  in  such  a 
way  that  when  positive  electricity  passes  in  the  direction 
Hg/HgCl  calomel  is  formed  and  Cl'  ions  disappear.  When 
the  current  passes  in  the  opposite  direction,  HgCl/Hg,  calomel 
disappears  and  an  equivalent  of  Cl'  ions  are  formed.  In 
other  words,  the  calomel  electrode  acts  like  an  electrode  of 
solid  chlorine,  as  already  mentioned.  As  the  mercury  is 
liberated  at  one  side  and  produced  at  the  other  in  equivalent 
quantity,  it  plays  no  essential  part  in  the  process. 

Theoretically,  only  calomel  (solid  and  in  solution)  and 
mercury  are  required  to  form  the  electrode,  but  potassium 
chloride  is  always  added  to  increase  the  conductivity  of  the 
solution.  As  the  tendency  of  Cl'  ions  to  enter  or  leave  the 
solution  depends  on  the  concentration  of  Cl'  ions  already 
present,  the  difference  of  potential  between  mercury  and  the 


ELECTROMOTIVE  FORCE 


375 


solution  must  depend  on  the  concentration  of  the  potassium 
chloride  solution  used.  A  normal  solution  is  mostly  largely 
employed. 

The  calomel  electrode  is  largely  used  as  a  normal  electrode 
by  means  of  which  the  E.M.F.s  of  other  electrodes  may  be  com- 
pared ;  its  chief  advantage  for  this  purpose  is  that  it  can  readily  be 
reproduced   with   an 
accuracy  of  about   i 
millivolt.     A  conven- 
ient form  of  the  elec- 
trode is  shown  in  Fig. 
42.     A  vessel  of  the 
type  already  described 
in    connection    with 
concentration       cells 
(p.    367)    may    con- 
veniently be  used.    A 
layer  of  dry  mercury 
is  first  placed  in  the 
bottom  of  the  vessel, 
then  a  paste  made  by 
rubbing  in  a  mortar 
mercury  and  calomel 
with  some  of  the  po- 
tassium chloride  solu- 
tion, and  the  vessel  is 
then  filled  up  with  ^-potassium  chloride  solution  which  has 
previously  been  saturated  with  calomel  by  shaking  with  excess 
of  the  latter.     Connection  with  the  mercury  may  conveniently 
be  made  by  means  of  a  platinum  wire  sealed  at  the  bottom  into  a 
glass  tube  A,  the  latter  passing  up  through  the  rubber  stopper 
closing  the  vessel.     In  making  measurements,   the  bent  side- 
tube,  C,  must  also  be  filled  with  the  potassium  chloride  solu- 
tion.    This  is  done  by  suction  at  the  straight  side-tube,  B, 
which  is  then  closed  by  a  clip. 


FIG.  42. 


376        OUTLINES  OF  PHYSICAL  CHEMISTRY 

For  measuring  the  potential  of  another  electrode  by  means 
of  the  calomel  electrode,  the  arrangement  already  shown  in 
Fig.  41  is  used. 

Neglecting  for  the  present  the  differences  of  potential  at  the 
liquid  junctions,  the  E.M.F.  of  the  combination  in  question  is 
the  algebraic  sum  of  the  differences  of  potential  at  the  two 
metal/solution  junctions.  It  follows  that  if  the  single  potential 
difference  between  mercury  and  solution  is  known,  the  single 
potential  difference  at  the  other  electrode  can  readily  be  cal- 
culated. Unfortunately  no  single  potential  difference  is  known 
with  certainty  (see  next  section),  and  it  is,  therefore,  necessary  to 
refer  them  to  an  arbitrary  standard.  Two  such  standards  are 
in  general  use,  (a)  the  so-called  "  absolute  "  standard ;  (&)  the 
hydrogen  standard.  As  regards  the  first  standard,  Ostwald  as- 
sumes that  the  potential  difference  between  mercury  and  the 
solution  in  the  normal  calomel  electrode  is  0*560  volts  at  18°, 
the  mercury  being  positive,  and  differences  of  potential  referred 
to  this  standard  are  termed  "  absolute  potentials  "  (see  next  sec- 
tion). On  the  other  hand,  Nernst  refers  E.M.F.s  to  the  hydrogen 
standard,  on  the  assumption  that  there  is  no  difference  of  poten- 
tial between  a  platinum  electrode  saturated  with  hydrogen  and  a 
normal  solution  of  an  acid.  The  "  absolute  "  potentials,  referred 
to  the  calomel  electrode,  have  a  theoretical  basis,  and  there  is 
reason  to  suppose  that  the  real,  but  at  present  unknown,  single 
potential  differences  are  not  very  different  from  the  "  absolute  " 
potentials.  Independently  of  this,  however,  the  use  of  the 
calomel  electrode  in  actual  measurements  is  justified  by  the 
fact  that  it  can  be  reproduced  with  a  high  degree  of  accuracy. 
The  use  of  the  hydrogen  electrode  as  standard  is  purely  arbi- 
trary, as  it  is  not  pretended  that  the  difference  of  potential 
between  electrode  and  solution  is  actually  zero,  but  the  refer- 
ence of  potential  differences  to  this  standard  has  certain  advan- 
tages. It  is,  in  fact,  usual  to  make  the  actual  measurements 
with  the  calomel  electrode,  and  then  to  refer  them  to  the 
hydrogen  standard,  on  the  basis  that  when  the  hydrogen 


ELECTROMOTIVE  FORCE  377 

electrode  is  taken  as  zero  the  E.M.F.  of  the  normal  calomel 
electrode  is  -  0-283  volts. 

In  order  to  illustrate  the  use  of  the  calomel  electrode  for 
potential  measurements,  the  separate  determination  of  the  dif- 
ferences of  potential  metal/solution  for  the  two  parts  of  the 
Daniell  cell  will  be  considered.  When  the  zinc  electrode  is 
combined  with  the  calomel  electrode,  as  shown  in  Fig.  41,  to 
form  the  cell 


Zn 


KC1        I  Hg2Cl2  in  I 
(in  vessel  C)  I      »KC1 


0*520  0-560 


i  -080 

the  E.M.F.  of  the  combination,  as  shown  by  potentiometer 
measurements,  is  1-080  volts,  the  zinc  being  negative  with 
regard  to  mercury,  so  that  positive  electricity  flows  in  the  cell 
from  zinc  to  mercury,  as  indicated  by  the  lower  arrow.  In 
order  to  obtain  the  potential  difference  Zn/ZnSO4,  we  proceed 
as  follows  (p.  365).  It  is  known  that  mercury  in  contact  with 
a  solution  of  calomel  becomes  positively  charged,  and  that  for 
the  calomel  electrode  the  tendency  for  positive  electricity  to 
pass  across  the  junction  towards  the  mercury  is  0*560  volts. 
The  tendency  for  positive  electricity  to  pass  round  the  circuit  is 
equivalent  to  1-080  volts,  hence  the  E.M.F.  at  the  Zn/ZnSO4 
junction  must  act  in  the  direction  shown  by  the  upper  left-hand 
arrow,  and  is  1-080  —  0*560  =  0-520  volts.  In  other  words,  the 
E.M.F.  at  the  junction  Zn/ZnSO4  is  0-520  volts,  the  zinc  being 
negatively  charged. 

Similarly,  the  observed  E.M.F.  of  the  cell 

Cu  |  «-CuSO4  |  KC1  |  Hg2Cl2  in  »-KCl  |  Hg 

0-585  0-560 

<  ------- 

0*025 


378        OUTLINES  OF  PHYSICAL  CHEMISTRY 

is  0-025  volts,  the  copper  being  positive  with  regard  to  mercury, 
hence  positive  electricity  flows  from  mercury  to  copper  in  the 
cell,  as  indicated  by  the  lower  arrow.  As  far  as  the  calomel 
junction  is  concerned,  the  tendency  for  positive  electricity  to 
flow  round  the  circuit  is  equivalent  to  0-560  volts  towards  the 
right,  as  indicated  by  the  arrow.  Hence  in  order  that  for  the 
whole  cell  the  tendency  of  positive  electricity  may  be  to  flow 
towards  the  left  at  a  potential  of  0-025  volts  the  E.M.F.  at  the 
Cu/CuSO4  junction  must  act  in  the  opposite  direction  to  that 
at  the  calomel  junction  and  exceed  it  by  0*025  volts.  The 
E.M.F.  at  the  junction  Cu/CuSO4  is  therefore  0-585  volts  and 
positive  electricity  flows  from  solution  to  copper,  as  indicated 
by  the  arrow. 

The  total  E.M.F.  of  the  cell  Zn/ZnSO4/CuSO4/Cu  is,  there- 
fore, -0-520  +  (  —  0*585)= —  1-105  volts,  which  agrees  with  the 
value  obtained  by  direct  measurement  (p.  344).  It  is  evident 
from  the  above  that  although  the  single  potential  differences  at 
the  junctions  depend  upon  the  value  of  the  potential  assumed 
for  the  standard,  the  E.M.F.  of  the  complete  cell  does  not 
depend  upon  the  E.M.F.  of  the  standard,  which  is  eliminated. 

If  referred  to  the  hydrogen  electrode  as  standard,  the  poten- 
tial difference  Zn/«"ZnSO4 is  -  0-520  +  (  -  0-283)  =  ~~  0*803 
volts,  and  that  for  Cu/wCuSO4  is  +  0-585  -f  (  -  0-283) 
=  +  0*302  volts,  the  E.M.F.  of  the  Daniell  cell  being  as  before 
=  (-0-803)  +  (  -  0-302)  =  -  1-105  volts. 

Single  Potential  Differences.  The  Capillary  Electro- 
meter— When  mercury  and  sulphuric  acid  are  in  contact  in  a 
capillary  tube,  and  the  arrangement  is  connected  with  a  source 
of  E.M.F.  in  such  a  way  that  the  mercury  is  in  contact  with 
the  negative  pole  and  the  acid  with  the  positive  pole,  the  area 
of  the  surface  of  separation  between  acid  and  mercury  tends  to 
diminish.  The  following  out  of  this  observation  of  Lippman's 
has  led  to  an  approximate  estimate  of  the  absolute  differences 
of  potential  at  metal/solution  junctions. 

When  mercury  and  sulphuric  acid  have  been  in  contact  for 


ELECTROMOTIVE  FORCE  379 

some  time,  it  is  probable  that  there  is  a  constant  difference  of 
potential  between  them,  brought  about  in  a  rather  complicated 
way.  We  have  already  learnt  that  well-defined  differences  of 
potential  are  established  when  a  metal  is  in  contact  with  a 
solution  of  one  of  its  salts  of  definite  concentration,  and  that 
is  probably  the  state  of  affairs  in  the  present  case.  We  may 
suppose  that  some  of  the  mercury  dissolves  in  the  sulphuric 
acid  to  form  mercurous  sulphate,  and  that  the  solution  im- 
mediately in  contact  with  the  mercury  is  saturated  with  regard 
to  the  salt.  As,  however,  the  osmotic  pressure  of  solutions  of 
mercury  salts  is  in  general  greater  than  the  solution  pressure 
of  mercury,  Hga"  ions  deposit  on  the  mercury  and  the  latter 
becomes  positively  charged  with  regard  to  the  solution.  The 
two  kinds  of  electricity  attract  each  other,  and  we  will  assume 
with  Helmholtz  that  the  effect  of  this  attraction  is  that  there  is 
a  layer  of  positive  electricity  near  the  surface  of  the  mercury 
holding  a  corresponding  layer  of  negative  electricity  near  the 
surface  of  the  acid  ("  Helmholtz  double  layer  ")  (cf.  Fig.  38). 

Now  there  will  be  a  certain  surface-tension  at  the  junction 
mercury/solution  in  the  capillary  tube,  and,  as  is  well  known, 
the  effect  of  surface  tension  is  to  make  the  areas  of  the  surfaces 
in  contact  as  small  as  possible.  This  tendency  will,  however, 
be  counteracted  by  the  electric  layers ;  the  positive  charges 
will  repel  each  other  and  tend  to  enlarge  the  surface,  and 
the  same  is  true  of  the  negative  charges.  The  effect  of  the 
difference  of  potential  is,  therefore,  to  diminish  the  surface 
tension.  The  fact  that  a  contrary  E.M.F.  applied  to  the 
junction  tends  to  diminish  the  surface  of  separation  between 
acid  and  mercury  will  now  be  readily  understood.  The  con- 
trary E.M.F.  diminishes  the  difference  of  potential  between 
acid  and  mercury,  part  of  the  force  diminishing  the  surface 
tension  is  removed,  and  the  latter  attains  more  nearly  its  true 
value  when  undisturbed  by  electrical  forces.  When  the  con- 
trary E.M.F.  is  gradually  increased,  the  surface  tension  increases 
at  first,  attains  a  maximum  value,  beyond  which  it  gradually 


380        OUTLINES  OF  PHYSICAL  CHEMISTRY 

diminishes.  It  is  plausible  to  suppose  that  the  surface  tension 
increases  as  the  difference  of  potential  between  mercury  and 
acid  gets  smaller  and  smaller,  that  it  attains  its  maximum  value 
when  the  contact  E.M.F.  at  the  junction  is  just  neutralized  by 
the  contrary  E.M.F.,  and  that  it  again  diminishes  as  the  latter 
is  further  increased  and  the  surfaces  become  charged  with 
electricity  of  opposite  sign  to  the  original  charges.  This  at 
once  gives  us  a  method  of  determining  single  differences  of 
potential.  It  is  only  necessary  to  note  when  the  surface  tension 
attains  its  maximum  value ;  under  these  circumstances  the 
applied  E.M.F.  is  clearly  equal  to  the  single  difference  of 
potential  at  the  junction  mercury/solution  and  the  problem 
as  to  the  value  of  a  single  potential  difference  is  solved.  In 
this  way  Ostwald  estimated  the  E.M.F.  of  the  normal  calomel 
electrode  at  0*560  volts. 

Unfortunately  the  matter  is  not  quite  so  simple  as  the  above 
considerations  would  lead  us  to  suppose,  and  it  is  fairly  certain 
that  the  absolute  potentials  arrived  at  in  this  way  may  differ 
considerably  from  the  true  values.  It  has  already  been  pointed 
out  that  two  standards  are  in  use,  and  that  the  use  of  the 
calomel  electrode  for  measuring  differences  of  potential  has 
certain  practical  advantages. 

Before  considering  another  method  which  has  been  suggested 
for  measuring  single  differences  of  potential,  it  should  be  men- 
tioned that  the  phenomena  just  described  have  been  applied 
to  the  construction  of  an  electrometer — the  so-called  capillary 
electrometer.  The  electrometer  consists  essentially  of  two 
quantities  of  mercury  between  which  is  placed  dilute  sulphuric 
acid.  One  quantity  of  mercury  is  in  contact  with  the  acid  at  a 
large  surface,  the  other  at  a  very  narrow  surface  in  a  capillary 
tube,  as  above  described.  When  the  apparatus  is  so  arranged 
that  the  mercury  and  acid  are  in  equilibrium  at  a  position  in 
the  capillary  tube,  and  the  two  quantities  of  mercury  are  then 
connected  with  a  source  of  E.M.F.,  the  potential  at  the  surface 
will  alter  owing  to  the  alteration  in  the  concentration  of  the 


ELECTROMOTIVE  FORCE  381 

rnercurous  salt  produced  by  the  current,  and  as,  owing  to  the 
alteration  of  the  surface  tension,  there  is  no  longer  equilibrium, 
the  position  of  the  surface  of  contact  will  alter. 

The  use  of  the  apparatus  as  an  electrometer  will  now  be 
evident.  It  is  best  so  to  arrange  matters  that  the  mercury  at  the 
narrow  surface  is  connected  with  the  negative  pole  of  the  external 
source  of  E.M.F.  through  a  tapping  key,  and  the  junction  is 
observed  through  a  small  microscope.  If  an  external  E.M.F.  is 
applied,  the  surface  will  move  when  the  key  is  momentarily 
depressed,  and  for  small  differences  of  potential  (up  to  0*01 
volt)  the  movement  of  the  meniscus  is  proportional  to  the  applied 
E.M.F.,  so  that  the  name  electrometer  is  justified.  When  the 
applied  E.M.F.  is  zero,  no  movement  of  the  meniscus  occurs  on 
making  contact,  and  the  electrometer  may  therefore  be  used  as 
a  null  instrument.  When  not  in  use,  the  electrometer  should 
be  connected  up  with  a  cell  of  E.M.F.  not  exceeding  i  volt. 

An  alternative  very  instructive  method  of  determining  single 
potential  differences,  the  theory  of  which  is  due  mainly  to 
Nernst  and  the  practical  realization  to  Palmaer,  will  now  be  de- 
scribed. When  mercury  in  a  fine  stream  is  allowed  to  flow  into 
an  electrolyte  containing  a  definite  concentration  of  rnercurous 
salt  (e.g.,  rnercurous  chloride),  Hga"  ions  from  the  solution 
deposit  on  the  drops  as  they  enter  (the  osmotic  pressure  of 
Hg2"  ions  in  the  solution  being  greater  than  the  solution  pres- 
sure of  the  mercury),  the  drops  thus  become  positively  charged, 
and  further  become  surrounded  with  a  layer  of  the  liberated 
Cl'  ions.  When  the  drops  reach  the  bottom  of  the  vessel 
containing  the  electrolyte,  the  positive  ions  are  given  up  and 
reunite  with  the  Cl'  ions  to  form  more  calomel.  The  net  result 
of  this  process  is  that  the  solution  gets  poorer  in  calomel  where 
the  drops  enter,  and  richer  where  they  unite  with  the  mercury. 
A  concentration  cell  is  thus  formed,  and  it  is  evident  that 
positive  electricity  must  flow  from  the  weak  to  the  strong 
solution,  that  is,  from  top  to  bottom  of  the  vessel,  a  deduction 
which  is  borne  out  by  experiment. 


382        OUTLINES  OF  PHYSICAL  CHEMISTRY 

Now  it  must  be  possible  to  reduce  the  concentration  of  Hg2m< 
ions  to  such  a  point  that  the  osmotic  pressure  of  the  Hg2" 
ions  is  just  equal  to  the  solution  pressure  of  the  mercury ;  there 
is  then  no  deposition  of  Hg2"  ions  on  the  entering  drops,  and  no 
current  flows.  Conversely,  when  no  current  results  when  mercury 
is  dropped  into  an  electrolyte  containing  Hg^'  tons,  the  difference 
of  potential  between  mercury  and  the  solution  must  be  zero.  If 
the  Hg2"  ion  concentration  is  still  further  reduced,  the  solution 
pressure  of  the  mercury  is  greater  than  its  osmotic  pressure 
in  the  solution,  and  the  current  flows  in  the  opposite  direction. 

The  Hg2"  ion  concentration  was  reduced  by  adding  potassium 
cyanide  till  the  point  of  no  current  and  therefore  zero  difference 
of  potential  was  reached.  The  solution  in  equilibrium  with 
mercury  under  these  conditions  may  be  termed  the  null  solu- 
tion. If  then  a  cell  is  built  up  of  the  type 

Hg  |  null  solution  |  solution  of  salt  of  metal  M  |  M 
o  <?!  *2 

e2,  the  difference  of  potential  between  metal  and  solution,  can 
be  determined  directly  if  the  E.M.F.  e1  at  the  junction  of  the 
solution  is  known  or  can  be  made  negligible. 

In  this  way  Palmaer  has  found  that  the  E.M.F.  at  the  junction 
Hg/«/ioKCl  saturated  with  Hg2Cl2  is  0-573  volts  at  18°,  cor- 
responding with  about  —0*520  volts  for  «/iKCl,  as  compared 
with  Ostwald's  value  of  0-560  volts. 

Some  writers  consider  that  the  problem  of  the  determination 
of  single  potential  differences  is  thus  finally  settled,  but  Palmaer 
himself  does  not  consider  that  all  the  difficulties  of  the  measure- 
ments have  been  overcome,  so  that  the  above  results  should 
only  be  taken  as  provisional.1 

Potential  Differences  at  Junction  of  Two  Liquids— Up 
to  the  present,  we  have  left  out  of  account  the  possible  dif- 
ferences of  potential  at  the  junction  of  two  solutions.  When 
the  E.M.F.  of  a  cell  is  considerable,  the  error  thus  arising  is 
only  slight,  but  if  the  E.M.F.  is  small,  as  for  many  concentra- 
1  Cf.  Palmaer,  Zeitsch.  physikal  Chem.,  1907,  59,  129. 


ELECTROMOTIVE  FORCE  383 

tion  cells,  the  potential  difference  at  the  liquid  contact  be- 
comes of  importance. 

It  has  been  shown  by  Nernst  that  in  many  cases  these  dif- 
ferences of  potential  can  be  calculated  according  to  his  theory 
of  electromotive  force,  and  the  results  obtained  in  this  way 
have  been  fully  confirmed  by  experiment.  The  calculation 
is  effected  most  readily  for  solutions  of  the  same  electrolyte 
in  different  concentrations,  for  example,  solutions  of  hydro- 
chloric acid.  When  the  solutions  are  brought  in  contact  the 
acid  will  tend  to  diffuse  from  the  more  concentrated  to  the  more 
dilute  solution.  As,  however,  the  acid  is  highly  ionized,  the 
H-  and  G'  ions  will  diffuse  independently,  and,  as  the  former 
move  the  more  rapidly,  the  dilute  solution  will  soon  contain  an 
excess  of  H*  ions  and  the  strong  solution  an  excess  of  Cl'  ions. 
Owing  to  the  electric  charges  conveyed  by  the  moving  ions, 
the  dilute  solution  will  become  positively  charged,  and  the 
strong  solution  negatively  charged.  However,  the  excess  of 
positive  electricity  in  the  dilute  solution  will  retard  the  entrance 
of  H'  ions  and  accelerate  the  Cl'  ions,  so  that  in  a  short  time 
the  ions  will  be  moving  at  the  same  rate.  The  difference  of 
potential  thus  produced  will  persist  until  both  solutions  attain 
the  same  concentration.  The  above  considerations  show  that 
the  contact  difference  of  potential  between  two  solutions  is  due  to 
the  different  migration  velocities  of  the  two  wns,  and  the  dilute 
solution  takes  the  potential  corresponding  with  that  of  the  more 
rapid  ion.  The  contact  difference  of  potential  between  dif- 
ferent solutions  of  the  same  salt  will  be  the  smaller  the  more 
nearly  the  speed  of  the  two  ions  agrees,  and  this  explains  why 
solutions  of  potassium  chloride  and  of  ammonium  nitrate  are 
used  as  connecting  solutions  in  potential  measurements  (com- 
pare p.  370). 

It  can  easily  be  shown  that  the  potential  difference  E  be- 
tween two  solutions  of  a  binary  electrolyte  with  univalent 
ions  (for  example,  hydrochloric  acid)  is  represented  by  the 
formula 


384        OUTLINES  OF  PHYSICAL  CHEMISTRY 
-r,       u  -  v  2*3026RT  c, 

•tt"~Jr     **»£ 

where  ^  and  cz  represent  the  ionic  concentrations  of  the  two 
solutions,  and  u  and  v  the  migration  velocities  of  the  anion 
and  cation  respectively.  From  the  above  equation  it  can  be 
calculated  that  the  contact  E.M.F.  between  N/io  and  N/ioo 
hydrochloric  acid  is  0*036  volt,  a  result  which  is  fully  con- 
firmed by  experiment. 

From  the  above  result,  the  value  of  E  may  be  calculated  for 
the  cell 

Ag  |  AgN03«/io  |  AgN03^/ioo  |  Ag 

when  the  contact  difference  of  potential  between  the  two 
solutions  is  not  practically  eliminated  by  the  use  of  potassium 
nitrate.  Taking  the  junctions  in  order,  we  have 

E  I  ^[  RT  loglo  &  +  ^  RT  loglo  4  -  RT  Iog10  9 

2-3o26r  u  -  v  £i_     ^j^RT1        _£ 

F      [  «  +  »  gl°  ^  ~  u  +  *>  gl°  - 


u  +  v 
for  room -temperature. 


2    X  0-0 


For  silver  nitrate  =  0-522  (p.  233),  c,    =  0-082,    c*  = 

u  -\-  i) 

0*0094.     Hence 

E  =  0*522  x  2  x  0-058  x  0-945  =  0-057  volts, 

in  excellent  agreement  with  the  value  found   experimentally, 
0-055  voltSi 

Gas  Cells — So  far  we  have  dealt  only  with  solid  substances 
and  amalgams  as  electrode  materials,  but  it  is  interesting  to 
note  that  gases  may  be  used  in  the  same  way.  This  is  made 
possible  by  using  metallic  electrodes,  usually  of  platinum  coated 
with  the  finely-divided  metal,  as  absorbents  for  the  gases.  The 


ELECTROMOTIVE  FORCE  385 

prepared  platinum  electrode  is  partially  immersed  in  the  solution 
of  an  electrolyte,  and  the  gas  is  bubbled  through  till  the  potential 
difference  between  electrode  and  solution  becomes  constant. 

As  an  example  of  a  gas  electrode,  the  hydrogen  electrode, 
already  referred  to,  will  be  described.  The  form  of  cell  repre- 
sented in  Fig.  41  may  be  used;  it  is  half  filled  with  normal 
acid,  the  platinum  pole,  held  by  a  well-fitting  cork,  is  partially 
immersed  in  the  acid,  and  hydrogen  gas  is  passed  in  by  the 
bent  side-tube  and  allowed  to  bubble  through  the  acid  for  ten 
or  fifteen  minutes  till  the  electrode  is  saturated.  The  straight 
side-tube,  which  has  been  open,  is  now  closed  by  a  clip,  and 
the  electrode  is  ready  for  use.  The  platinum  pole  itself  usually 
consists  of  a  piece  of  platinum  foil  joined  by  hammering  to  a 
platinum  wire,  the  latter  being  sealed  into  the  bottom  of  the 
glass  tube  carried  by  the  cork  closing  the  cell.  Electrical  con- 
nection may  be  made  by  a  copper  wire  passing  down  through 
the  glass  tube  and  dipping  into  a  little  mercury  at  the  bottom, 
the  mercury  being  also  in  contact  with  the  upper  part  of 
the  platinum  wire  which  projects  into  the  interior  of  the  glass 
tube. 

The  electrode  is  completely  reversible  and  behaves  like  a 
plate  of  metallic  hydrogen.  When  positive  electricity  passes 
from  solution  to  metal,  hydrogen  ions  are  discharged  accord- 
ing to  the  equation  2H*  ->  H2 ;  when  it  goes  in  the  contrary 
direction  gaseous  hydrogen  becomes  ionised  according  to  the 
converse  equation,  H2  ->  2H-. 

A  hydrogen  concentration  cell  is  obtained  when  two  hy- 
drogen electrodes,  containing  the  gas  at  different  pressures,  are 
combined  in  the  usual  way.  Such  cells  correspond  exactly  with 
those  made  up  with  amalgams  of  different  concentrations,  and 
the  E.M.F.s  can  be  calculated  by  the  same  formula  (p.  371). 
The  direction  of  the  current  is  such  that  the  pressures  on  the 
two  sides  tend  to  become  equal,  so  that  hydrogen  becomes 
ionised  at  the  high  pressure  side  and  is  discharged  as  gas  at 
the  low  pressure  side. 
25 


386       OUTLINES  OF  PHYSICAL  CHEMISTRY 

Concentration  cells  with  oxygen,  sulphuretted  hydrogen  and 
other  gases  have  also  been  investigated. 

Cells  in  which  the  electrodes  are  in  contact  with  different 
gases,  for  example,  the  hydrogen-oxygen  cell,  are  referred  to 
below. 

Potential  Series  of  the  Elements — During  the  considera- 
tion of  the  Daniell  cell  (p.  360),  it  was  pointed  out  that  metals 
differ  greatly  with  regard  to  their  solution  pressures.  Zinc,  for 
example,  has  a  very  high  solution  pressure,  whilst  that  of  copper 
is  very  small. 

The  difference  of  potential  between  a  metal  and  a  solution  of 
one  of  its  salts  at  room  temperature  is  represented  by  the 
formula 

T?      °'°58  i        p 
"IT  logioj> 

and  if/,  the  osmotic  pressure  of  the  positive  ions  of  the  salt,  is 
the  same  for  all  the  electrodes,  say  that  represented  by  a  normal 
solution  of  a  salt,  it  is  evident  that  the  value  of  E  is  propor- 
tional to  the  solution  pressure  of  the  metal.  As  regards  the 
standard  to  which  the  E.M.F.s  are  to  be  referred,  the  hydrogen 
standard  has  in  this  case  certain  advantages.  The  potential  of 
metals  with  regard  to  normal  solutions  of  their  salts  is  therefore 
obtained  by  measuring  the  E.M.F.  of  cells  of  the  type 

H2(Pt)  |  «H-  |   normal  solution  of  the  metallic  salt  |  metal, 

the  difference  of  potential  H2(Pt)  |  «H-  being  taken  as  zero. 
The  E.M.F.  of  the  combination 

H2(Pt)  |  nH-  |  n  '  ZnS04  |  Zn 


0770 

measured  with  the  potentiometer  in  the  usual  way,  is  0770 
volts,  the  hydrogen  being  positive  with  regard  to  the  zinc. 
The  value  of  Ezn-Znso4  is  therefore  -  0770  volts,  the  poten- 
tial difference  at  the  other  junction  being  zero  by  definition, 


ELECTROMOTIVE  FORCE  387 

and  positive  electricity  goes  in  the  cell  in  the  direction  indicated 
by  the  arrow,  that  is,  the  solution  tension  of  zinc  is  greater  than 
that  of  hydrogen,  so  that  the  former  displaces  the  latter  (indirectly] 
from  solution. 

On  the  other  hand,  the  E.M.F.  of  the  cell 

H2(Pt)  |  «H-  |  «CuSO4  |  Cu 

0-329 

is  0-329  volts,  copper  being  positive ;  positive  electricity  goes  in 
the  solution  in  the  direction  represented  by  the  arrow.  Hydro- 
gen therefore  goes  into  solution  and  copper  is  deposited,  so  that 
the  solution  pressure  of  hydrogen  is  greater  than  that  of  copper. 
In  an  exactly  corresponding  way,  the  potential  of  any  other 
metal  may  be  determined.  The  following  table  contains  what 
is  termed  the  potential  series  of  some  important  elements. 
The  numbers  represent  the  potential  difference,  in  volts,  between 
a  metal  and  a  normal  solution  of  one  of  its  salts,  referred  to 
the  hydrogen  electrode  as  standard.  For  those  elements  with 
a  higher  solution  pressure  than  hydrogen  the  numbers  have  the 
negative  sign,  for  a  reason  which  has  already  been  given, 
(p.  xvii.). 

Na      Mg        Al       Mn        Zn        Cd        Fe        Co        Ni 

-2 -58- I -482 -I '2  76 -I -075 -0'7  70 -0-420 -0*334 -0-23  2 -0-2  28 

Pb        H2       Cu         Hg         Ag          I  Br          Cl 

-  0-151  ±  o  +  0-329     0-753     Q'771     °'52°     °'993     J'353 
The  numbers  for  chlorine,  bromine  and  iodine,  are  comparable 
with  the  others,  and  are  obtained  in  a  somewhat  similar  way. 
The  value  for    chlorine,   for   example,   may    be    obtained    by 
measuring  the  E.M.F.  of  a  cell  of  the  type. 

H2(Pt)  |  »  •  H-  |  *  •  Cl  |  Cl2(Pt), 

the  right-hand  electrode  being  reversible  for  chlorine  just  as  the 
left-hand  one  is  reversible  for  hydrogen  (see  below). 

By  means  of  this  table,  the  E.M.F.  of  a  cell  made  up  of  two 


Zn  |  nZn"  \  «Ag*  |  Ag 


0*770  0-771 


388       OUTLINES  OF  PHYSICAL  CHEMISTRY 

metals  in  contact  with  normal  solutions  of  their  salts  can  at 
once  be  calculated.  As  the  following  schemes  show,  a  zinc- 
nickel  element  has  the  E.M.F.  0*770  —  0*228  =  0*542  volts, 
and  a  zinc-silver  element  the  E.M.F.  0*770  -  (  —  0*771)  = 
1-541  volts. 

Zn  |  nZn"  \  «Ni"  |  Ni 
0*770  0*228 

0*542  v.  i'54i  v. 

positive  electricity  flowing  in  the  respective  cells,  in  the  direc- 
tions indicated  by  the  lower  arrows.  The  student  should  have 
no  difficulty  in  understanding  these  schemes  in  the  light  of  the 
considerations  advanced  on  p.  365.  Both  in  the  case  of  zinc 
and  of  nickel  the  solution  pressure  of  the  metal  is  greater  than 
the  osmotic  pressure  of  the  metallic  ions  in  normal  solution,  and, 
therefore,  when  arranged  to  form  a  cell,  the  tendency  for  posi- 
tive electricity  to  pass  round  the  circuit  is  in  the  opposite  direc- 
tion at  the  two  junctions.  Positive  electricity,  therefore,  flows 
in  the  direction  in  which  the  acting  force  is  the  greater,  and  the 
total  E.M.F.  is  the  difference  of  the  forces  at  the  two  junctions. 
In  the  zinc-silver  cell,  on  the  other  hand,  the  forces  act  in  the 
same  direction,  and  the  total  E.M.F.  is  therefore  the  sum  of  the 
forces  at  the  junctions. 

It  is  evident  from  the  above  that  metals  which  stand  higher 
than  hydrogen  in  the  tension  series  can  liberate  hydrogen  from 
acids,  and  the  numbers  in  the  table  are  a  measure  of  the  energy 
of  the  reaction.  On  the  other  hand,  hydrogen  at  atmospheric 
pressure  should  displace  the  metals  which  stand  below  it  in 
the  tension  series,  and  it  has  been  proved  by  experiments  with 
platinized  platinum  electrodes  saturated  with  hydrogen  that 
such  is  the  case. 1  Further,  each  metal  is  able  to  displace  from 
combination  any  metal  below  it  in  the  tension  series  under 
equivalent  conditions,  and  the  difference  of  potential  between 
the  metals  is  a  measure  of  the  free  energy  of  the  change. 

1  That  the  changes  do  not  take  place  readily  under  ordinary  con- 
ditions is  doubtless  due  to  the  reaction  velocity  being  small. 


ELECTROMOTIVE  FORCE  389 

Cells  with  Different  Gases — The  simplest  example  of 
these  cells  is  the  hydrogen-chlorine  cell,  already  referred  to. 
One-half  of  the  cell  consists  of  a -hydrogen  electrode  in  acid, 
the  other  of  a  similar  electrode  saturated  with  chlorine,  and 
the  two  electrodes  are  combined  as  represented  in  Fig.  41,  the 
intermediate  vessel  containing  acid  of  the  same  strength  as  that 
in  the  cell.  The  chemical  change  which  takes  place  in  the  cell 
is  the  combination  of  hydrogen  and  chlorine  to  form  hydro- 
chloric acid.  Representing  the  cell  as  usual — 

H2(Pt)  |  «H-  |  «Cr  |  Cl2(Pt), 


it  is  clear  that  positive  electricity  flows  in  the  cell  from  hydrogen 
to  chlorine  in  the  direction  represented  by  the  arrow,  the 
chlorine  becoming  the  positive  and  the  hydrogen  the  negative 
pole.  The  E.M.F.  of  the  cell  in  normal  acid  at  the  ordinary 
temperature  is  about  1*35  volts. 

The  most  important  cell  of  this  type  is  the  hydrogen-oxygen 
or  Grove's  cell,  the  two  poles  being  saturated  with  hydrogen 
and  oxygen  respectively.  When  connection  is  made  the  gases 
gradually  disappear,  hydrogen  becoming  ionized  at  one  pole 
and  oxygen  uniting  with  water  to  form  hydroxyl  ions  at  the 
other  pole.  The  cell  may  therefore  be  represented  by  the 
following  scheme — 


H,(Pt) 


water 


(acid,  alkali  or  salt) 


02(Pt) 


1-23 

and  positive  electricity  flows  through  the  cell  from  hydrogen  to 
oxygen  as  represented  by  the  arrow,  so  that  hydrogen  is  the 
negative  pole  and  oxygen  the  positive  pole.  The  hydrogen 
electrode  is  reversible  with  regard  to  hydrogen,  as  follows : 
H2^2H',  the  reaction  taking  place  at  the  oxygen  electrode 
is  as  follows :  H2O  +  $O2^2OH'.  When  employed  as  indicated 


390       OUTLINES  OF  PHYSICAL  CHEMISTRY 

above,  the  change  is  that  represented  by  the  two  upper  arrows 
and  2F  passes  through  the  wire;  when,  on  the  other  hand,  2F 
is  sent  through  the  cell  in  the  opposite  direction,  the  changes 
at  the  two  poles  are  represented  by  the  two  lower  arrows. 

There  is  reason  to  suppose  that  if  absolutely  indifferent 
electrodes  were  used  for  absorbing  the  gases,  and  the  changes 
at  the  electrodes  were  fully  reversible,  the  E.M.F.  of  the  cell 
would  be  1*23  volts.1  The  values  actually  observed  are  smaller, 
probably  owing  to  the  formation  of  an  oxide  of  platinum,  which 
has  an  oxygen  potential  different  from  that  of  free  oxygen. 

Theoretically,  only  pure  water  is  necessary  as  electrolyte,  but,in 
order  to  increase  the  conductivity,  dilute  acid  or  alkali  or  a  dilute 
salt  solution  is  employed  as  electrolyte.  The  E.M.F.  of  the  cell 
is  independent  of  the  nature  of  the  electrolyte,  but  this  is  not 
the  case  for  the  single  potential  differences  at  the  electrodes. 

Oxidation-Reduction  Cells — The  gas  cell  just  described 
is  a  typical  oxidation-reduction  cell,  as  when  working  hydrogen 
is  being  oxidized  at  the  negative  pole  and  oxygen  reduced  at 
the  positive  pole. 

As  may  be  anticipated,  corresponding  cells  can  be  con- 
structed in  which  instead  of  hydrogen  another  reducing  agent 
is  used,  and  instead  of  gaseous  oxygen  another  oxidizing  agent. 
Indifferent  metals,  such  as  platinum  or  iridium,  are  used  as 
electrodes  in  all  cases. 

We  will  first  consider  a  cell  built  up  of  a  hydrogen  electrode 
on  one  side  and  a  platinized  platinum  electrode  dipping  in  a 
solution  of  a  ferrous  and  a  ferric  salt  on  the  other.  When  the 
two  electrodes  are  connected  up,  a  current  flows  in  the  cell 
from  the  hydrogen  to  the  other  electrode.  Hence  at  the 
hydrogen  electrode  gaseous  hydrogen  is  going  into  solution 
as  hydrogen  ions  according  to  the  equation  H2  +  2F  =  2H*,2 
and  at  the  other  electrode  Fe"'  ions  are  being  reduced  to  Fe" 
ions  according  to  the  equation  2Fe"-  -  2F  =  2Fe",  the  charges 
neutralizing  each  other  through  the  wire  and  thus  producing 
1  Corresponding  with  the  free  energy  of  formation  of  water  from  its 
elements. 

22F  or  2  x  96,540  coulombs  converts  a  mol  of  hydrogen  to  H-  ions. 


ELECTROMOTIVE  FORCE  391 

a  current.  When  the  same  quantity  of  electricity  is  passed 
through  the  cell  in  the  opposite  direction,  Fe"  ions  are  con- 
verted to  Fe—  ions,  and  hydrogen  gas  is  liberated  at  the  other 
pole  ;  the  cell  therefore  works  reversibly,  and  the  measurement 
of  the  E.M.F.  gives  a  measure  of  the  free  energy  or  affinity  of 
the  reaction.  The  total  change  is,  of  course,  expressed  by  the 
equation  2Fe*"  +  H2  =  2Fe"  +  2H\ 

Other  oxidizing  agents  can  be  measured  in  the  same  way 
against  the  hydrogen  electrode,  and  from  the  results  a  table 
of  various  solutions,  arranged  in  the  order  of  their  oxidizing 
potentials,  can  be  obtained.  Some  of  the  values  obtained  in 
this  way  may  be  given. 

SnCl2  in  HC1  0-23  volts     FeCl3  in  HC1  0-98  volts 

NH2OH  in  HC1       0-38  volts     KMnO4  in  H2SO4       i  -50  volts 

The  above  are  only  meant  to  indicate  the  order  of  the  results, 
as  the  accurate  values  depend  greatly  on  the  concentration  and 
composition  of  the  solutions. 

The  four  solutions  mentioned,  even  stannous  chloride,  in 
acid  solution  exert  an  oxidizing  action  on  gaseous  hydrogen, 
and  therefore  the  direction  of  the  current  is  the  same  as  in  the 
ferric  chloride  cell.  As  might  be  anticipated,  potassium  per- 
manganate has  the  highest  oxidation  potential. 

When,  on  the  other  hand,  a  platinum  electrode  dipping  into 
a  solution  of  stannous  chloride  in  potassium  hydroxide  is  con- 
nected with  a  hydrogen  electrode  so  as  to  form  a  cell 

Sn"  in 


H2(Pt) 


«OH' 


(Pt) 


hydrogen  ions  are  discharged  and  the  stannous  salt  becomes 
oxidized,  positive  electricity,  therefore,  flowing  in  the  cell  in  the 
direction  of  the  arrow.  The  change  which  takes  place  in  the 
cell  may  be  represented  by  the  equation  2!!'  +  Sn"  =Sn""  +  H2, 
the  hydrogen  acting  as  the  oxidizing  agent.  In  this  case  we 


392       OUTLINES  OF  PHYSICAL  CHEMISTRY 

may  say  that  the  stannous  chloride  solution  has  a  certain  reduc- 
tion potential. 

The  above  considerations  are  sufficient  to  show  that  the 
terms  "  oxidizing  agent  "  and  "  reducing  agent  "  are  relative  and 
not  absolute ;  whether  a  substance  acts  as  an  oxidizing  or  a 
reducing  agent  depends  on  the  substance  with  which  it  is 
brought  in  contact. 

The  hydrogen  electrode  may  be  replaced  by  a  platinum 
electrode  dipping  in  a  solution  of  a  reducing  agent,  an  oxida- 
tion-reduction cell  containing  only  liquids  being  obtained.  One 
well-known  cell  of  this  type  consists  of  platinum  electrodes 
dipping  in  solutions  of  ferric  chloride  and  stannous  chloride 
respectively.  The  changes  at  the  electrodes  may  be  represented 
by  the  equations 

(i)  2Fe-  -  2F  =  2Fe"     (2)  Sn"  +  2F  =  Sir- 
and  the  total  change  as  follows — 

2Fe-  +  Sn-  =  2Fe"  +  Sir- 
It  is  now  easy  to  understand  what  at  first  sight  appears  very 
puzzling,  that  a  ferric  salt  can  oxidize  a  stannous  salt  at  a  dis- 
tance, the  solutions  being  in  separate  cells  and  possibly  con- 
nected by  an  indifferent  solution.  The  above  equations  show 
that  the  essential  feature  of  the  phenomenon  is  the  transference 
of  two  positive  charges  from  the  iron  to  the  tin  ions  through 
the  wire. 

As  a  definite  potential  may  be  ascribed  to  every  substance 
acting  as  an  oxidizing  or  reducing  agent,  it  is  clear  that  the 
E.M.F.  of  an  oxidation-reduction  cell  may  be  represented  as 
the  algebraic  sum  of  the  differences  of  potential  at  the  two  junc- 
tions. When  a  strong  oxidizing  solution  is  combined  with  a  still 
stronger  oxidizing  solution  to  form  a  cell,  the  former  will  be 
oxidized  at  the  expense  of  the  latter,  but  the  E.M.F.  of  the  cell 
will  be  small,  as  the  solutions  are  acting  against  each  other. 
The  further  apart  two  solutions  are  in  the  oxidation-reduction 
potential  series,  the  greater  will  be  the  E.M.F.  of  the  cell  formed 
by  their  combination. 


ELECTROMOTIVE  FORCE  393 

We  are  now  in  a  position  to  give  a  clear  definition  of  oxida- 
tion and  reduction  in  dilute  salt  solutions.  A  substance  is 
oxidized  when  it  takes  up  positive  charges  or  loses  negative 
charges,  a  substance  is  reduced  when  it  takes  up  negative 
charges  or  loses  positive  charges.  The  usual  definition  of 
oxidation  as  consisting  in  an  addition  of  oxygen  to  a  compound 
or  the  abstraction  of  hydrogen  from  it,  is  clearly  inapplicable 
to  salt  solutions,  and  the  above  definition  affords  a  satisfactory 
representation  of  the  observed  phenomena.  On  the  other 
hand,  the  older  definition  retains  its  value  for  changes  in  which 
organic  compounds  are  concerned,  and  for  solid  compounds; 
these  have  so  far  been  very  little  investigated  from  an  electro- 
chemical standpoint. 

Electrolysis  and  Polarization — If  an  external  E.M.F.  of 
i  volt  is  applied  to  two  platinum  electrodes  dipping  in  a  con- 
centrated solution  of  hydrochloric  acid,  it  will  be  found  that 
the  large  current  which  at  first  passes  when  connection  is  made 
rapidly  diminishes  and  finally  falls  practically  to  zero.  The  ex- 
planation of  this  behaviour  is  that  while  the  current  is  passing 
hydrogen  accumulates  on  the  cathode  and  chlorine  on  the 
anode,  thus  setting  up  an  E.M.F.  which  acts  against  the  E.M.F. 
applied  to  the  poles  of  the  cell.  This  phenomenon  is  termed 
polarization.  In  the  above  case  the  gases  go  on  accumulat- 
ing in  the  electrodes  till  the  back  E.M.F.,  which  we  will  term  e, 
is  equal  to  the  applied  E.M.F.,  when  the  current  ceases.  If, 
however,  an  E.M.F.  of  1*5  volts  is  applied  at  the  electrodes,  a 
continuous  current  passes  through  the  solution  and  it  is  evident 
that  in  this  case  the  back  E.M.F.  e  has  not  attained  the  value 
of  i '5  volts.  The  explanation  is  evident  when  it  is  remem- 
bered that  the  E.M.F.  of  a  cell  in  which  platinum  electrodes 
are  charged  with  hydrogen  and  chlorine  respectively  at  atmo- 
spheric pressure  is  1-35  volts  (p.  389).  When  an  E.M.F 
of  i -5  volts  is  applied,  the  electrodes  become  charged  up  tc 
atmospheric  pressure,  but  no  higher,  the  excess  of  the  gases 
escaping  into  the  atmosphere.  It  follows  that  e  cannot  under 


394       OUTLINES  OF  PHYSICAL  CHEMISTRY 

ordinary  circumstances  attain  a  higher  value  than  1*35  volts,  so 
that  electrolysis  proceeds  at  an  E.M.F.  of  E  —  e  =  0*15  volts. 

The  E.M.F.  which  must  just  be  exceeded  in  order  that  a 
continuous  current  may  pass  through  an  electrolyte  is  termed 
the  "  decomposition  potential"  of  the  electrolyte,  and  it  is  clear 
from  the  above  example  that  the  decomposition  potential  is  equal 
to  the  E.M.F.  of  a  cell  in  which  the  products  of  electrolysis  are 
the  combining  substances.  As  the  E.M.F.  of  such  a  cell  is  the 
algebraic  sum  of  the  differences  of  potential  at  the  electrodes,  it 
is  clear  that  the  decomposition  potential  is  also  the  sum  of  two 
factors,  namely,  the  sum  of  the  potentials  required  to  discharge 
the  anion  and  cation  respectively. 

The  decomposition  potential  of  an  electrolyte  may  be  deter- 
mined in  two  ways.  According  to  the  first  method,  the  external 
E.M.F.  applied  to  the  electrodes  is  gradually  raised  and  the 
point  noted  at  which  there  is  a  sudden  increase  in  the  current. 
The  value  of  the  current,  C,  is  determined  by  the  equation 

E  -  e  =  CR, 

where  R  is  the  resistance  of  the  circuit,  and  will  obviously 
increase  rapidly  as  soon  as  E  is  greater  than  e.  The  second 
method  is  to  charge  the  electrodes  up  to  atmospheric  pressure 
by  using  an  E.M.F.  greater  than  e,  then  the  external  circuit  is 
broken  and  the  E.M.F.  of  polarization  measured  at  once.  This 
method  depends  upon  the  fact  already  indicated,  that  the  de- 
composition potential  is  that  E.M.F.  which  is  just  sufficient  to 
overcome  the  E.M.F.  of  polarization. 

-As  has  just  been  pointed  out,  the  potential  required  to  dis- 
charge an  ion  such  as  Zn"  must  just  exceed  the  difference  of 
potential  at  the  junction  Zn/Zn",  and  is,  therefore,  the  same  as 
the  potential  of  the  metal  in  volts  in  the  tension  series  (p.  387). 
Further,  the  E.M.F.  required  to  decompose  an  electrolyte  is 
clearly  the  sum  of  the  separate  differences  of  potential  required 
to  discharge  the  anion  and  cation  respectively,  and  is,  there- 
fore, obtained  by  adding  the  values  for  the  two  ions  in  the 


ELECTROMOTIVE  FORCE  395 

tension  series.  The  matter  becomes  clearer  when  we  consider 
that  the  potential  difference  between  an  element  and  its  ions 
may  conveniently  be  regarded  as  a  measure  of  the  affinity  of  the 
element  for  electricity.  Thus  the  affinity  of  zinc  for  positive 
electricity  is  equivalent  to  0770  volts,  and  that  of  chlorine  for 
negative  electricity  to  1*353  volts.  To  convert  zinc  ions  to 
metallic  zinc  we  must,  therefore,  apply  a  contrary  E.M.F.  which 
just  exceeds  the  affinity  of  zinc  for  positive  electricity,  in  other 
words,  the  decomposition  potential  of  zinc  ions  is  0*770  volts. 

On  this  basis,  the  decomposition  potential  of  zinc  chloride 
should  be  0-770  +  1*353  =  2 '123  volts,  of  hydrochloric  acid 
1-353  volts,  and  of  copper  chloride  (-0-329  +  1*353)  =  1*024 
volts  respectively.  This  is  fully  confirmed  by  the  experimental 
determinations  of  Le  Blanc,  who  obtained  the  following  values : 
ZnCl2  =2-15  volts,  HC1  =  1*31  volts,  CuCl2  =  1*05  volts,  an 
agreement  within  the  limits  of  experimental  error. 

Separation  of  Ions  (particularly  Metals)  by  Electro- 
lysis— The  results  just  mentioned  are  well  illustrated  by  the 
phenomena  observed  when  a  mixture  of  electrolytes  is  electro- 
lysed at  different  values  of  the  applied  E.M.F.  The  foregoing 
considerations  show  that  on  gradually  raising  the  E.M.F.  that 
chemical  change  takes  place  most  readily  for  which  the  least 
difference  of  potential  is  required,  and  this  may  be  taken 
advantage  of  for  the  electrolytic  separation  of  metals  which  are 
discharged  at  different  potentials.  Suppose,  for  example,  a 
mixture  of  hydrochloric  acid,  zinc  and  copper  chlorides  is 
subjected  to  electrolysis.  Below  i  volt  practically  no  change 
will  occur,  but  at  1*1  volts,  a  little  above  the  decomposition 
potential  for  copper  chloride,  copper  will  be  deposited  on  the 
cathode.  When  it  has  been  almost  completely  removed,  and 
the  potential  is  raised  to  1*4  volts,  hydrogen  will  be  liberated 
at  the  cathode.  Finally,  the  attempt  may  be  made  to  remove 
zinc  by  raising  the  external  E.M.F.  above  2*2  volts,  but  this 
cannot  be  effected  in  acid  solution,  as  there  is  a  large  excess 
of  hydrogen  ions,  which  are  more  easily  discharged  than  zinc. 


396       OUTLINES  OF  PHYSICAL  CHEMISTRY 

In  an  exactly  corresponding  way,  almost  all  the  bromine 
may  be  electrolytically  separated  from  a  solution  containing 
zinc  chloride  and  zinc  bromide  before  the  chlorine  appears. 

It  is,  therefore,  clear  that  it  is  the  value  of  the  E.M.F.,  and 
not  the  strength  of  the  current,  which  is  of  primary  importance 
for  the  separation  of  metals,  and  in  recent  years  methods  based 
on  this  principle  have  become  of  great  commercial  importance. 
Besides  the  value  of  the  applied  E.M.F.,  the  concentration  of 
the  ions  in  contact  with  the  cathode  is  of  great  importance, 
as  the  decomposition  potential  necessarily  depends  on  the  ionic 
concentration,  and  hence  great  attention  is  now  paid  to  the 
efficient  stirring  of  the  electrolyte.1 

The  Electrolysis  of  Water — It  is  an  experimental  fact 
that  when  aqueous  solutions  of  many  strong  acids  and  alkalis 
are  electrolysed,  only  hydrogen  and  oxygen  are  liberated  as 
products  of  electrolysis,  and  the  decomposition  potential,  the 
E.M.F.  which  must  be  applied  in  order  to  liberate  these  gases 
in  appreciable  amount,  is  about  i'66  volts.  It  has  usually  been 
considered  that  one  or  both  of  these  gases  are  formed  by  the 
action  of  the  primary  products  of  electrolysis  on  the  solvent, 
but  this  does  not  account  for  the  fact  that  the  decomposition 
potential  is  in  general  the  same  for  different  acids  and  bases. 
Le  Blanc  and  Nernst,  on  the  other  hand,  consider  that  the  gases 
are  a  product  of  the  primary  decomposition  of  water.  As 
already  mentioned,  water  is  ionised  according  to  the  equation 
H2O;±H'  +  OH'  and  also,  though  to  a  much  smaller  extent, 
according  to  the  equation  OH'^H*  -f  O".  By  special  methods 
it  can  be  shown  that  water  can  be  split  up  at  i  •  i  volts  (which 
corresponds  approximately  with  the  potential  of  the  hydrogen- 
oxygen  cell)  (p.  370),  and  Nernst  considers  that  the  chemical 
change  then  taking  place  is  the  discharge  of  H*  and  divalent 
O"  ions ;  the  electrolysis  is  very  slow  because  of  the  exceedingly 

!The  electrolytic  separation  of  metals  on  this  principle  is  described  in 
recent  papers  by  Sand  (Journal  of  the  Chemical  Society,  1907,  91,  373, 
1908,  93,  1572),  and  others. 


ELECTROMOTIVE  FORCE  397 

minute  concentration  of  the  O"  ions.  The  more  rapid  decom- 
position at  1-66  volts  is  due  to  the  discharge  of  H-  and  OH'  ions 
the  latter  combining  to  form  water  and  oxygen  according  to  the 
equation  2 OH'  =  H2O  +  O.  At  a  still  higher  potential,  when 
sulphuric  acid  is  used  as  electrolyte,  SO4"  ions  are  discharged, 
and  the  evolution  of  oxygen  becomes  still  more  vigorous.  Al- 
though there  is  some  evidence  in  favour  of  the  views  just 
indicated,  the  electrolytic  decomposition  of  water  does  not 
seem  yet  to  be  thoroughly  understood1 

Accumulators — As  is  well  known,  accumulators  are  em- 
ployed for  the  storage  of  electrical  energy.  An  accumulator  is 
a  reversible  element ;  when  a  current  is  passed  through  it  in  one 
direction  the  electrodes  become  polarized,  and  when  the  polar- 
izing E.M.F.  is  removed  and  the  poles  of  the  accumulator  are 
connected  by  a  wire,  the  products  of  electrolysis  recombine  with 
production  of  a  current  and  the  cell  slowly  returns  to  its  original 
condition. 

It  will  be  clear  from  the  above  that  the  Grove's  gas  cell  is  a 
typical  accumulator  or  secondary  element;  when  a  current  is 
passed  through  it  in  one  direction  the  electrodes  become 
charged  with  hydrogen  and  oxygen,  and  these  gases  can  be 
made  to  recombine  with  production  of  a  current.  From  a 
technical  point  of  view,  however,  a  satisfactory  accumulator 
must  retain  its  strength  unaltered  for  a  long  time  when  the 
poles  are  not  connected,  and  must  be  easily  transported.  A  gas 
accumulator  would  be  in  many  respects  un suited  for  commercial 
purposes. 

The  apparatus  most  largely  used  for  the  storage  of  electricity 
is  the  lead  accumulator,  the  electrodes  of  which  in  the  un- 
charged condition  contain  a  large  amount  of  lead  sulphate 
(obtained  by  the  action  of  sulphuric  acid  on  the  porous  lead  of 
which  the  electrodes  largely  consist  at  first)  and  dip  in  dilute 
sulphuric  acid.  The  accumulator  is  charge  by  sending  an 
electric  current  through  it.  At  the  cathode,  the  lead  sulphate 
is  reduced  by  the  hydrogen  ions  (or  rather  by  the  discharged 
hydrogen)  to  metallic  lead  according  to  the  equation 

1  Compare  Foerster,  Zeitsch.  physikal.  Chem.,  1909,  69,  236. 


398       OUTLINES  OF  PHYSICAL  CHEMISTRY 

PbSO4  +  2H-  -  2F  =  Pb  +  2H-  +  SO4" 
or  more  simply,  PbSO4  -  2F  =  Pb  +  SO4" 
On  the  other  hand,  the  SO4"  ions  wander  towards  the  anode 
and  react  with  it  according  to  the  equation 

PbSO4  +  SO4"  +  2H2O  +  2F  =  PbO2  +  4H-  +  2SO4" 

so  that  the  anode  and  cathode  consist  mainly  of  lead  peroxide 
and  metallic  lead  respectively. 

On  connecting  up  to  obtain  a  current  (discharging),  SO4"  ions 
are  discharged  at  the  new  anode  (the  lead  pole),  and  reconvert 
it  to  lead  sulphate,  according  to  the  equation 

Pb  +  SO4"  +  2F  =  PbSO4, 

and  simultaneously  H*  ions  are  discharged  at  the  new  cathode 
(the  peroxide  pole),  the  peroxide  being  reduced  to  the  oxide, 
and  acted  on  by  sulphuric  acid  to  reform  the  sulphate,  according 
to  the  equation 

PbO2  +  2H-  +  H2SO4  -  2F  =  PbSO4  +  2H2O. 

The  chemical  changes  taking  place  on  charging  and  discharging 
are  summarized  in  the  equation 

Pb  +  PbO2  +  2H2SO4^2PbSO4  +  2H2O ; 

the  upper  arrow  represents  discharging,  and  the  lower  arrow 
charging. 

The  E.M.F.  of  the  lead  accumulator  is  about  2  volts.  It  is 
not  strictly  reversible,  but  under  ordinary  conditions  of  working 
about  90  per  cent,  of  the  energy  supplied  and  stored  up  in  it 
can  again  be  obtained  in  the  form  of  work. 

The  Electron  Theory l — In  the  previous  chapters  we  have 
learnt  that  certain  atoms  (or  groups  of  atoms)  can  become 
associated  with  definite  quantities  of  electricity,  and  that  certain 
other  atoms  can  take  up  twice  as  much,  three  times  as  much, 
and  so  on.  No  atom  is  associated  with  less  positive  electricity 

iNernst,  Theoretical  Chemistry,  chap.  ix. ;  Rutherford,  Radio-Activity; 
Ramsay,  Presidential  Address,  Trans.  Chem.  Soc.,  1908,  93,  774. 


ELECTROMOTIVE  FORCE  399 

than  a  hydrogen  atom,  and  we  may  therefore  state  that  a 
hydrogen  atom  unites  with  unit  quantity  of  electricity  to  form 
an  ion.  A  barium  ion  has  twice  as  much  positive  electricity, 
and  a  ferric  ion  three  times  as  much  positive  electricity  as 
a  hydrogen  ion.  Further,  since  quantities  of  hydrogen  and 
chlorine  ions  in  the  proportion  of  their  atomic  weights  are 
electrically  equivalent,  it  follows  that  Cl'  (and  other  univalent 
negative  ions)  contain  unit  quantity  of  negative  electricity. 

This  increase  by  steps  in  the  amount  of  electricity  associated 
with  atoms  at  once  recalls  the  law  of  multiple  proportions, 
and  it  appears  plausible  to  ascribe  an  atomistic  structure  to 
electricity ;  in  other  words,  to  postulate  the  existence  of  positive 
and  negative  electrical  particles,  which  under  ordinary  cir- 
cumstances are  associated  with  matter.  On  this  view,  the 
number  of  dots  or  dashes  ascribed  to  positive  and  negative 
ions  respectively  indicates  the  number  of  electrical  particles 
(positive  or  negative)  with  which  the  atoms  become  associated 
to  form  ions. 

These  views1  (Helmholtz,  1882)  have  received  powerful 
support  during  the  last  few  years  from  the  results  of  experi- 
ments on  the  passage  of  electricity  through  vacuum  tubes,  the 
so-called  Hittorf  s  or  Crookes'  tubes.  When  a  current  at  very 
high  potential  is  sent  through  a  highly  evacuated  tube,  rays 
from  the  cathode — the  so-called  cathode  rays — stream  across 
the  tube  with  great  velocity,  and  it  has  been  shown  that  these 
rays  consist  of  negative  electricity.  The  speed  of  the  particles 
depends  on  the  E.M.F.  between  the  poles  of  the  tube,  but 
at  a  difference  of  potential  of  10,000  volts  is  about  one-fifth 
of  the  velocity  of  light.  The  mass  of  these  particles  is  about 
i/ 1 ooo  of  that  of  the  hydrogen  atom.  They  are  usually 
termed  negative  electrons.  More  recently,  it  has  been  dis- 
covered that  the  /?  rays  given  off  from  disintegrating  radium 
at  a  speed  approaching  that  of  light  also  consist  of  negative 
electrons. 

1  Helmholtz,  Faraday  Lecture,  Trans.  Chem.  Soc.,  1882. 


400        OUTLINES  OF  PHYSICAL  CHEMISTRY 

As  negative  electrons  have  thus  been  found  to  exist  separate 
from  matter,  it  is  natural  to  expect  that  free  positive  electrons 
may  also  be  isolated.  So  far,  however,  this  has  not  been 
found  possible,  and  opinions  differ  somewhat  as  to  the  reason. 
Nernst,  following  Helmholtz,  considers  that  there  is  no  ground 
for  doubting  the  existence  of  positive  electrons ;  the  reason  why 
it  has  not  yet  been  found  possible  to  isolate  them  is  due  to 
their  great  affinity  for  matter.  Further,  Nernst  and  others 
assume  that  positive  and  negative  electrons  unite  to  form 
neutral  atoms  or  neutrons,  and  that  these  neutrons  constitute 
the  ether  which  is  assumed  to  pervade  all  space.  Other 
investigators  regard  a  positive  ion  as  an  atom  minus  one  or 
more  negative  electrons ;  the  loss  of  a  negative  electron  would 
leave  the  previously  neutral  atom  positively  charged.1  From 
observations  on  the  effect  of  a  magnetic  field  on  the  cathode 
discharge,  it  has  been  calculated  that  the  actual  charge  carried 
by  a  univalent  ion  (positive  or  negative)  is  about  4  x  10  ~  10 
electrostatic  units. 

The  application  of  the  electron  theory  to  ordinary  chemical 
changes  yields  interesting  results.  For  simplicity  we  will  assume 
the  existence  of  positive  electrons,  and  designate  them  by  the 
symbol  ©,  negative  electrons  by  the  symbol  0.  When  hydro- 
gen arid  chlorine  unite  to  form  hydrochloric  acid,  we  assume 
that  under  ordinary  conditions  the  valency  of  the  hydrogen 
is  satisfied  by  that  of  the  chlorine.  We  may,  however,  dis- 
place a  chlorine  atom  by  a  positive  electron,  and  thus  obtain 
the  saturated  chemical  compound  H  0  or  H  • ;  in  an  exactly 
similar  way,  the  hydrogen  may  be  displaced  by  a  negative 
electron,  forming  the  saturated  compound  Cl©.  In  the 
same  way,  a  dilute  solution  of  copper  sulphate  contains  the 


saturated  compounds  Cu/        or  Cu  -  and  SO4<^        or  SO4". 

The  electrons,  therefore,  behave  exactly  as    univalent  atoms, 
1  Ramsay,  loc.  cit. 


ELECTROMOTIVE  FORCE  401 

the  positive  electrons  enter  into  combination  with  positive 
elements  such  as  H,  K,  Na,  Ba,  etc.,  the  negative  electrons  enter 
into  combination  with  negative  elements  or  groups,  such  as 
Cl,  Br,  I,  NO3,  SO4.  Nothing  is  known  as  to  the  constitution 
of  a  non-ionised  salt  molecule  in  solution.  The  formula  for 
non-ionised  sodium  chloride  may  perhaps  be  Na  ©0C1,  the 
molecule  being  held  together  at  least  partly  by  electrical  forces. 

Just  as  there  are  great  differences  in  the  affinity  of  the 
elements  for  each  other,  so  the  elements  have  very  different 
affinity  for  electrons.  Zinc  and  the  other  metals  have  a  great 
affinity  for  positive  electrons,  the  so-called  non-metallic  ele- 
ments have  in  many  cases  considerable  affinity  for  negative 
electrons.  The  order  of  the  elements  in  the  tension  series  may 
be  regarded  as  the  order  of  their  affinity  for  electricity.  On  this 
view  the  potential  required  to  discharge  the  ions  is  simply  the 
equal  and  opposite  E.M.F.  required  to  overcome  the  attraction 
of  the  element  and  the  electron  (p.  375). 

Practical  Illustrations.  Dependence  of  Direction  of  Current 
in  Cell  on  Concentration  of  Electrolyte — It  has  already  been 
pointed  out  (p.  346)  that  the  current  in  a  Daniell  cell  may  be 
reversed  in  direction  by  enormously  reducing  the  Cu"  ion  con- 
centration by  the  addition  of  potassium  cyanide.  The  two  chief 
methods  for  diminishing  ionic  concentration  are  (i)  the  forma- 
tion of  complex  ions  (as  in  the  above  instance) ;  (2)  the  forma- 
tion of  insoluble  salts. 

When  a  ceil  of  the  type 


Cd 


CdSO4 

dilute 


KNO 


CuS04 
dilute 


Cu 


is  set  up,  and  the  pc4es  are  connected  through  an  electroscope, 
it  will  be  found  that  positive  electricity  passes  in  the  cell  in  the 
direction  of  the  arrow.  If  some  ammonium  sulphide  solution 
is  then  added  to  the  copper  sulphate  solution,  "insoluble" 
copper  sulphide  is  formed,  and  the  concentration  of  the  Cu" 
26 


402        OUTLINES  OF  PHYSICAL  CHEMISTRY 

ions  is  reduced  to  such  an  extent  that  the  current  flows  in  the 
reverse  direction. 
If  the  Daniell  cell 


Zn 


ZnSO4     KNO3     CuSO4 


dilute 


dilute 


Cu 


is  built  up  in  the  same  way,  it  will  not  be  found  possible  to  re- 
verse the  current  by  the  addition  of  ammonium  sulphide,  owing 
to  the  greater  solution  pressure  of  the  zinc  as  compared  with 
cadmium ;  but  if  potassium  cyanide  is  added,  the  current 
changes  in  direction,  owing  to  the  fact  that  the  Cu"  ion  con- 
centration in  a  strong  solution  of  potassium  cyanide  (in  which 
the  copper  is  mainly  present  in  the  complex  anion  Cu(CN)4") 
is  considerably  less  than  in  a  solution  of  copper  sulphide. 

The  following  experiments,  which  are  described  in  consider- 
able detail  in  the  course  of  the  chapter,  should  if  possible  be 
performed  by  the  student.  For  further  details  text-books  on 
practical  physical  chemistry  should  be  consulted. 

(a)  Preparation  of  a  standard  cadmium  cell  (p.  357). 

(b)  Measurement  of  the  E.M.F.  of  a  cell  by  the  compensation 
method  (p.  355). 

(c)  Preparation  and  use  of  a  calomel  "half-cell"  (p.  375). 

(d)  Preparation  and  use  of  a  capillary  electrometer  (p.  380). 

(e)  Measurement  of  the  E.M.F.    of  a   concentration  cell 
(p.  368). 

(/)  Measurement  of  the  E.M.F.  of  the  hydrogen-oxygen 
cell  (p.  389). 

(g)  Determination  of  the  solubility  of  a  difficultly  soluble 
salt,  e.g.,  silver  chloride,  by  E.M.F.  measurements  (p.  370). 


PROBLEMS 

1.  A  certain  quantity  of  a  gas  measures  TOO  c.c.  at  25°  and  700 
mm.  pressure.     What  pressure  will  be  required  to  change   the 
volume  to  50  c.c.  at  -  10°  C.  ?  Ans.     1236  mm. 

2.  What  volume  is  occupied  by  (a)  I  gram  of  nitrogen,  (6)   i 
gram   of  carbon  dioxide  at  20°   and   a   pressure  of   72    cm.  of 
mercury?  Ans.     (a)  906*3  c.c.  ;  (6)  576*8  c.c. 

3.  An  open  vessel  is  heated  till  one-third  of  the  air  it  contains 
at  20°  is  expelled.     What  is  the  temperature  of  the  vessel  ? 

Ans.     117-6°  C. 

4.  If  0*5  grams  of  a  gas  measure  65  c.c.  at  10°  and  500  mm. 
pressure,  what  is  its  molecular  weight  ?  Ans.     271*5 

5.  If  i  gram  of  nitrogen,  i  gram  of  oxygen  and  0*2  gram   of 
hydrogen  are  mixed  in  a  volume  of  2*24  litres  at  o°,  calculate  the 
respective  partial  pressures  of  the  gases  in  the  mixture,  in  grams 
per  sq.  cm.  Ans.     369,  323,  and  1025  grams,  cm.2 

6.  The  density  of  benzyl  alcohol,  C6H5CH2OH,  at  its  boiling- 
point  is  1*145.     Compare  the  observed  and  calculated  values  of 
the  molecular  volume  (p.  61).         Ans.     Obs.  123*7.     Calc.  128*8. 

7.  The  density  of  a  solution  containing  4*1375  grams  of  iodine 
in  100  grams  of  nitrobenzene  is  1*2389  at  18°,  the  density  of  the 
solvent  at  the  same  temperature  being  1*20547.     From  these  data 
calculate  the  molecular  solution  volume  of  iodine. 

Ans.     67*2  c.c. 

8.  The  density  of  formic  acid  at  20°  is  1*2205  and  nD  at  the  same 
temperature  is  1*3717.     Calculate  the    molecular   refractivity  of 
formic  acid  by  the  Lorentz  formula  and  compare  it  with  the  value 
calculated  from  the  atomic  refractivities  (cf.  p.  65). 

Ans.     Obs.  8*56.     Calc.  8*35. 

g.  The  value  of  no  for  a  mixture  of  formic  acid  and  water  con- 
taining 62*7  per  cent,  of  the  latter  was  found  to  be  1*3625  at  19.5°, 
and  the  density  at  the  same  temperature  1*1462.  Calculate  the 
refraction  constant  by  the  Lorentz  formula  and  compare  it  with 
that  calculated  on  the  assumption  that  the  components  exert  their 
effects  independently.  [D19°  for  water  0*9984  ND=  1*3333.] 

Ans.     Obs.  0*1937.     Calc.  0*1936. 
403 


404        OUTLINES  OF  PHYSICAL  CHEMISTRY 

10.  Find  the  relationship  between  the  solubility,  s,  of  a  gas  and 
its  absorption  coefficient,  a,  in  a  liquid  at  t°  (cf.  p.  83). 

Ans.     s 


11.  Calculate  the  gas  constant,  R,  in  litre-atmospheres  from  the 
observation  that  a  solution  containing  34-2  grams  of  cane  sugar 
in  i  litre  of  water  has  an  osmotic  pressure  of  2-522  atmospheres 
at  20°.  Ans.     0*0860. 

12.  The  osmotic  pressure  of  a  2  per  cent,  solution  of  acetone  in 
water  is  equal  to  590  cm.  of  mercury  at  10°.     What  is  the  mole- 
cular weight  of  acetone  ?  Ans.     60  (found),  58*0  (theor.). 

13.  What  is  the  molecular  concentration  of  an  aqueous  solution 
of  urea  which  at  20°  exerts  an  osmotic  pressure  of  4-6  atmos- 
pheres ?  Ans.     0-19  molar. 

14.  The  vapour  pressure  of  ether  (mol.  wt.  74)  is  lowered  from 
38-30  cm.   to  36-01  cm.  by  the  addition  of  11*346  grams  of  tur- 
pentine to  100  grams  of  ether.     Calculate  the  molecular  weight 
of  turpentine.  Ans.     132  (theor.  138). 

15.  The  vapour  pressure  of  water  at  50°  is  92  mm.      How  much 
urea  (mol.  wt.  60)  must  be  added  to  100  grams  of  water  to  reduce 
the  vapour  pressure  by  5  mms.  ?  Ans.     i8'i  grams. 

16.  A  current  of  dry  air  was  passed  in  succession  through  a 
bulb  containing  a  solution  of  30  cane  sugar  in  160  grams  of  water, 
through  a  bulb,  at  the  same  temperature,  containing  water,  and 
finally  through   a  tube   containing  concentrated  sulphuric  acid. 
The  loss  of  weight  in  the  water  bulb  was  .0-0315  grams  and  the 
gain  in  weight  in  the  sulphuric  acid  bulb  3-02  grams.     Calculate 
the  molecular  weight  of  cane  sugar  in  the  solution.          Ans.  339. 

17.  The  addition  of  1-065  grams  of  iodine  to  30*14  grams  of 
ether  raises  the  boiling-point  of  the  latter  by  0-296°.    What  is  the 
molecular  weight  of  iodine  in  ether  ?  Ans.     251. 

18.  The   vapour  pressure  of  ether   at  o°  is  183-4  mm.,  at  20° 
433*3  mm.     Calculate  the  latent  heat  of  vaporisation  per  mol.  of 
ether  at  10°.  Ans.     6840  cal. 

[Use  the  formula  d\ogepldT  =  -  q  /RT2,  where  p  is  the  vapour 
pressure  of  the  liquid  at  the  absolute  temperature  T  andq  is 
the  latent  heat  of  vaporisation  per  mol.  of  liquid.  Integrating 
between  the  absolute  temperatures  Tj  and  T2  (the  correspond- 
ing pressures  being  pl  and^2)  we  have  (cf.  p.  166), 


19.     The  vapour  pressure  of  water  over  a  mixture  of  CuSO4, 
5H2O  and  CuSO4,  3H2O  is  2*933  mm.  at  13*95°  and  21701  mm.  at 


PROBLEMS  405 

397°.    Calculate  the  heat  given  out  when  i  mol.  of  water  combines 
with  CuSO4,  3H2O  to  form  CuSO4,  5H2O.  Ans.     -  13,730  cal. 

20.  0*3  grams  of  camphor,  C10H16O,   added  to  25*2  grams   of 
chloroform  raise  the  boiling-point  of  the  solvent  by  0*299°.     Cal- 
culate the  molecular  elevation  constant  for  chloroform. 

Ans.    38*2. 

21.  From  the  data  in  the  previous  question  calculate  the  heat 
of  vaporisation  of  chloroform  (boiling-point  61°).    Ans.     6931  cal. 

22.  1*2  grams  of  a  substance  dissolved  in  24*5  grams  of  water 
(K=i8*5)  caused  a  depression  of  the  freezing-point  of  1*05°.    Find 
the  molecular  weight  of  the  substance.  Ans.     86. 

23.  Beckmann  found  that  0*0458  grams  of  benzoic  acid  in  15 
grams  of  nitrobenzene  (K  =  8o)  caused  a  depression  of  the  freez- 
ing-point of  0*099°.     What  conclusion  can  be  drawn  from  this  ob- 
servation as  to  the  molecular  condition  of  benzoic  acid   in  nitro 
benzene  ?  Ans.     Acid  is  associated. 

24.  At  343°  the  vapour  pressure  of  ammonium  bromide  is  195 
mm.  and  at  356°  it  is  289  mm.    Calculate  the  heat  of  vaporisation 
of  ammonium  bromide,  assuming  dissociation  complete. 

Ans.    45,000  cal. 

25.  From  formula  (i)  p.  137,  deduce  the  expression 

loo  Hs    dT  . 


and  hence  calculate  the  osmotic  pressure  of  an  ethereal  solution 
the  boiling-point  of  which  is  35*2°.  (Boiling-point  of  ether,  34-8°  ; 
latent  heat  of  vaporisation  per  gram.  84-5  cal.  Ans.  6*5  atmos. 

26.  At  21°  the  surface  tension,  y,  of  diethyl  sulphate  in  28*28 
dynes/cm.2  and  at  62*6°  y  is  24*00  dynes/cm.2    Find  the  value  of  c, 
the    temperature   coefficient   of    the   molecular    surface   energy 
(D21  =  1*0748;  D82*6=  1*0278).  Ans.     2*17. 

27.  For    monochlorhydrin     y    at    17°     is     47*61    dynes/cm.2 
(0=1*3254)   and   at  57*8°  43*72   dynes/cm.2  (0  =  1*2883).      What 
conclusions  can   be  drawn  from  these  data  as  to  the  molecular 
complexity  of  the  liquid?  Ans.     c=i'44,  liquid  is  associated. 

28.  Calculate  the  heats  of  formation  of  ethane,  ethylene  and 
acetylene  respectively  from  their  elements  at  17°  (a)  at  constant 
pressure,  (b)  at  constant  volume  from  the  following  data.     Heats 
of  combustion  :  ethane  370,440  cal.,  ethylene  333,350  cal.,  acety- 
lene 310,059  cal.    Heats  of  formation  :  carbon  dioxide  94,300  cal., 
liquid  water  68,400  cal.,  all  at  constant  pressure. 

Ans.  Ethane:  C.  P.  23,360  cal.,  C.V.  21,  910  cal.  Ethyl- 
ene :  C.P.  -  7950  cal,  C.V.  -  9210  cal.  Acetylene  :  C.  P. 
-53,059  cal.,  C.V.  -  5^,189  cal. 

29.  Find  the  heat  of  formation  of  anhydrous  aluminium  chloride 
from  the  following  data  (Thomsen). 


406        OUTLINES  OF  PHYSICAL  CHEMISTRVT 

aAl+6HClAg«zAlCl,+3Ha+239,76ocal. 

H2+Cl2=2HCl  +  2X44,ooo  cal. 
HCl  +  Ag=HClAg+ 17,315  cal. 
AlCl3+Ag=AlCl3Ag  + 76,845  cal. 

Ans.     321,960  cal.  (for  A12C16). 

30.  The   heat  of  solution  of  anhydrous  strontium  chloride  is 
11,000   cal.,  that  of  the  anhydrous  salt -7,300  cal.     What  is  the 
heat  of  hydration  of  the  anhydrous  salt  to  hexahydrate. 

Ans.     18,300  cal. 

31.  The  vapour  density  of  phosphorus  pentachloride  referred  to 
air  as  unity  was  found  to  be  5*08  at  182°,  4*00  at  250°,  and  3*65  at 
300°,    calculate    the    degrees    of  dissociation    at   these   tempera- 
tures. Ans.     41*7  per  cent.  ;  80  per  cent.  ;  97  -3  per  cent. 

32.  From  the  following  data  for  the  equilibrium  N2O4  ^  2NO2 
at  49'7°.     Calculate  the  degree  of  dissociation    at  each  pressure 
and  show,  by  finding  the  dissociation   constant,  that  the  law  of 
mass  action  applies  : — 

Pressure  in  mm.  Hg      26*80      9375       182*69      261-37      497*75 
Density  (air  =i)  1*663       1*788         1*894        1'993        2*144 

The  vapour  density  of  N2O4  is  3*179  (air  =  i). 

Ans.     0-93  ;  0*789 ;  0-69  ;  0*63  ;  0*493. 

33.  Bodenstein  found  that  the  degree  of  dissociation  of  carbonyl 
chloride,  according  to  the  equation  COC12  *j^  CO  +  Cla,  is  67  per 
cent,  at  503°,  80  per  cent,  at  553°,  and  91  per  cent,  at  603°     From 
these    results   calculate    the    heat   of  idissociation    of    carbonyl 
chloride. 

Ans.      19,210    cal.    from     5O3°-553° ;   22,880    cal.    from 
553°-6o3°. 

34.  The  ratio  of  distribution  of  aniline  between  benzene  and 
water  is  10*1  :  i.     When  a  litre  of  aniline  hydrochloride  solution, 
containing   0*0997  mols.   of  the  salt,  was  shaken  with  59  c.c.  of 
benzene  at  25°  it  was  found  that  50  c.c.  of  benzene  had  taken  up 
0*0648  grams  of  aniline.      Find  the  amount  of  hydrolysis  of  ani- 
line hydrochloride  in  the  solution  and  calculate  the  dissociation- 
constant  of  aniline  as  a  base  (cf.  p.  291). 

Ans.     1-56  per  cent.,  4*6  x   lo"10. 

35.  When  heated  in  aqueous  solution  at  52*4°  the  concentration 
of  sodium  bromoacetate  in  solution  was  11*0,  9*4,  7*9  and  6*9  at 
times  o,  26,  52  and  74  hours  respectively  from  the  commencement 
of  the  reaction,  the    decomposition   being   ultimately    complete. 
Find  the  order  of  the  reaction  and  calculate  the  times  required  to 
complete  (a)  one-third,  (b)  two-thirds  of  the  change. 

Ans.     Unimolecular.    47*5  hours,  139  hours. 


PROBLEMS  407 

36.  In  an  experiment  on  the  rate  of  reaction  between  sodium 
thiosulphate  and  ethyl  bromoacetate  (cf.  p.  232)  50  c.c.  of  the  re- 
action mixture  required  the  following  amounts  of  p'ono  N  iodine 
at  the  times  from  the  commencement  of  the  reaction  indicated  in 
the  table. 

t  (min.)  o  5        10          15        25        40          oc 

cc.s.  iodine  solution     37*25     247     1875     15*3     11*6      8*85     4*4 
Show  that  the  reaction  is  of  the  second  order  and  find  the  velo- 
city constant  for  concentrations  of  i  mol.  per  litre.       Ans.     14*6. 

37.  From  the  electrolysis  of  hydrochloric  acid  in  a  cell  with  a 
cadmium  anode  the  following  results  were  obtained  :  change  in 
concentration   of  chlorine    at    anode    and    cathode    respectively 
+  O'oo545  gram  silver  deposited  in  voltameter  connected  in  series 
with  the  cell  0*0986  gram.     Calculate  the  transport  numbers  of 
hydrogen  and  chlorine  (Cl  =  35*46;  Ag  =  107-9). 

Ans.     H  =  0-832  ;  Cl  =  0-168. 

38.  Find  the  degree  of  ionisation  of  lactic  acid  at  different  dilu- 
tions and  calculate  the  ionisation   constant   from  the   following 
data,  valid  for  25°  : — 

v  (litres)        64  128  256  512  <x 

HV  34*3          47*4          64-2          87*6          360 

Ans.     0*000138. 

39.  If  the  velocity  coefficient  for  catalysis  by  N/4  acetic  acid  is 
0*00075  what  will  be  the  coefficient  when  the  solution  is  also  N/4O 
with  respect  to  sodium  acetate,  assuming  that  the  latter  is  dis- 
sociated to  the  extent  of  86  per  cent.  ?  Ans.     0*000067. 

40.  If  an  amount  of  base  insufficient  for  complete  saturation  is 
added  to  an  equimolecular  mixture  of  acetic  and  glycollic  acid,  in 
what   proportion  will   the    salts  be  formed.       (Dissociation  con- 
stants at  25°.     Acetic  acid  0*000018,  glycollic  acid  0-00015.) 

Ans.     i  :  2*9. 

41.  A  N/io  solution  of  sodium  acetate  is  ionised  to  the  extent 
of  80  per  cent,  at  18°.     What  is  the  osmotic  pressure  of  the  solu- 
tion at  this  temperature  ?  Ans.     4*28  atmos. 

42.  Sodium  chloride  in  0*2  molar  solution  is  dissociated  to  the 
extent  of  80  per  cent,  at  18°.    What  will  be  the  concentration  of  a 
urea  solution  which  is  isotonic  with  the  salt  solution  ? 

Ans.     21*6  grams  per  litre. 

43.  Calculate  the  E.  M.  F.  of  an  oxyhydrogen  cell  from  the 
facts  that 

2H2  +  O2  =  2H2O  +  2  x  68,400  cal. 

and  that  the  temperature  coefficient  of  the  E.  M.  F.  of  the  cell  is 
-0*00085  volts  at  room  temperature  (17°).  Ans.     1*23  volts. 


408        OUTLINES  OF  PHYSICAL  CHEMISTRY 

44.  Find  the  P.  D.  at  each  electrode  and  the  total  E.  M.  F.  of 
the  cell 

Ag/AgCl  sat.  sol./NiSO4  o'i  molar/Ni. 

at  25°,  assuming  that  the  P.  W.  at  the  liquid  contact  is  eliminated 
and  that  the  nickel  salt  is  60  per  cent,  ionised.  The  normal 
potential.  E.  P.,  for  silver  is  -  0*771  volt  and  for  nickel  +  0*228 

RT  P 

volt  (cf.  p.  387).     [Use  the  formula  E  =  E.  P.  +  ^-log*  ^.] 

nr          C2 

Ans.     Ag  electrode  +  0771  -  0*289  =  +  0*482  volts. 

Ni         „          -  0*228  -  0*035  =  ~  0*263  volts. 

Total  E.  M.  F.  of  cell  -  0*745  volts. 


INDEX 


ABNORMAL  molecular  weights  in  solu- 
tion, 123. 

—  vapour  densities,  40-42. 
"Absolute"  potentials,  376,  380,  382. 
Absorption  of  light,  69-73. 

—  spectra  and  chemical  constitution, 

Accumulators,  397. 

Acetic  acid,  adsorption  of,  325. 

atomic  volume  of,  61. 

density  of  vapour,  41. 

—  —  dissociation  of,  267. 

Acids,   catalytic  action    of,   205,   219, 
272. 

—  effect  of  substitution  on  strength 
of,  304. 

—  strength  of,  269-274. 
Active  mass,  156. 

of  solids,  173. 

Additive  properties,  62,  251,  335. 
Adsorption,  324. 

—  and  enzyme  action,  332. 

—  and  surface  tension,  330. 

—  by  charcoal,  324. 

—  formulae,  328. 

—  theories  of,  324-328. 
Affinity,  chemical,  148,  154,  271. 

—  constant,  157,  273,  275. 
Amalgams,  cells  with,  351. 
Amicrons,  318. 

Ammonium  chloride,    dissociation  of, 
42,  219. 

—  hydrosulphide,      dissociation      of, 
176. 

Argon,  position  in  periodic  table,  23. 
Associated  solvents,  ionising  power  of, 

339- 

Associating  solvents,  123. 
Assocation  in  gases,  41. 

—  in  solution,  124,  338-342. 
Atomic  heat,  21. 

—  hypothesis,  5. 


Atomic  refractions,  values  of,  65. 

—  volumes,  60. 

—  weights,  determination  of,  8-15. 

—  —  standard  for,  17. 
table  of,  19. 

Attraction,  molecular,  34,  58. 
Available  energy,  104,  150,  352. 
Avidity  of  acids,  269-274. 
Avogadro's  hypothesis,  10,  36. 

deduction    of,     from     kinetic 

theory  of  gases,  32. 

valid  for  solutions,  103,  109. 

BASES,  catalytic  action  of,  220. 

—  strength  of,  274-276,  292. 
Beckmann's  methods,  116,  120. 
Benzoic    acid,     distribution     between 

solvents,  178,  198. 
Beryllium  (glucinum),  atomic    weight 

of,  10,  it. 

Bimolecular  reactions,  207,  230. 
Binary  mixtures  of  liquids,  84-91. 

distillation  of,  87. 

vapour  pressure  of,  87. 

Blood,  catalysis  by,  202,  229, 
Boiling-point,  elevation  of,  114  118. 
Boron,  atomic  heat  of,  12. 
Brownian  movement,  318. 

CADMIUM  standard  cell,  356. 
Calomel  electrode,  373. 
Calorimeter,  146,  147,  153. 
Capillary  electrometer,  380. 
Cane  sugar,  hydrolysis  of,  205. 
Carbon,  atomic  heat  of,  12. 

—  dioxide,    critica     phenomena    of, 
49. 

Catalysis,  217-224. 

—  mechanism  of,  222*. 

—  technical  importance  of,  219. 
Cathode  rays,  399. 

Chemical  affinity,  148,  154,  271, 


409 


410       OUTLINES  OF  PHYSICAL  CHEMISTRY 


Chemical    equilibrium    and    pressure, 
169. 

and  temperature,  166,  169. 

Clark  cell,  358. 
Coagulation  of  colloids,  320. 

adsorption  theory  of,  323. 

Colligative  properties,  62. 
Colloidal  particles,  charged,  319. 

size  of,  318,  323. 

—  platinum,  220,  232,  316. 

—  solutions,  313. 

coagulation  of,  319. 

filtration  of,  323. 

optical  properties  of,  317. 

preparation  of,  315. 

Colloids,  313. 

—  diffusion  of,  313. 

—  electrical  properties  of,  319. 

—  irreversible,  323. 

—  precipitation  by  electrolytes,  319. 

—  reversible,  323. 
Combining  proportions,  law  of,  4. 

—  volumes  of  gases,  law  of,  9. 
Combustion,  heat  of,  145. 
Complexions,  281,  303,  310. 
Components,  definition  of,  181. 
Concentration  cells,  367-373. 
Conductivity,  electrical,  effect  of  tem- 
perature on,  263. 

equivalent,  251. 

of  pure  substances,  258. 

measurement  of,  254-258. 

—  molecular,  249,  257,  265. 

—  specific,  235,  249. 
Conservation  of  energy,  law  of,  140. 

—  of  mass,  law  of,  3. 
Constant  boiling  mixtures,  89. 
Constitutive  properties,  62. 
Continuity  of  gaseous  and  liquid  states, 

Copper  sulphate,  hydrates  of,  174. 
Corresponding  states,  law  of,  56. 

—  temperatures,  57. 
Critical  constants,  51,  56. 

—  phenomena,  49-58,  69. 

—  solution  temperature,  86. 

—  temperature,  determination  of,  77. 
Carbohydrates,  188. 
Crystallisation  interval,  192. 
Crystalloids,  313. 

"  Cyclic"  processes,  133,  136. 

DANIELL  cell,  348,  362,  366. 

reversal  of  current  in,  366,  401. 

Decomposition  potential  of  electrolytes, 
394: 


Deliquescence,  175. 

Density  of  gases  and  vapours,  36,  43. 

determination  of,  37,  41,  48^ 

Dialysed  iron,  315. 

Dialysis,  315. 

Dielectric  constant,  225,  338. 

and  ionisation,  338. 

Diffusion  of  gases,  33. 

—  in  solution,  108. 

and  osmotic  pressure,  98,  io3. 

Dispersed  system,  315. 
Dispersion,  315. 
Dissociating  solvents,  123. 
Dissociation  constant,  266,  273,  275. 

—  electrolytic,  260-263,  335-337. 
degree  of,  261. 

evidence  for,  335-337. 

mechanism  of,  342. 

of  water,  283,  293. 

—  of  salt  hydrates,  174. 

—  in  gases,  42,  125,  163. 
solution,  125,  260-263. 

—  thermal,  163. 

Distillation  of  binary  mixtures,  87,  91. 

—  steam,  90. 

Distribution  coefficient,   95,  178,   197, 

327- 

Dulong  and  Petit's  law,  n. 
Dyeing,  adsorption  theory  of,  330-331. 

EFFLORESCENCE,  175. 
Electrode,  calomel,  373. 

—  hydrogen,  376,  385. 
Electrodes,  normal,  375,  376. 
Electrolysis,  236-238,  393. 

—  of  water,  396. 

—  separation    of    metals,    etc.,    by, 

395- 

Electrolytes,  strong,  279-282. 
Electrolytic    dissociation.       See    Dis- 
sociation, electrolytic. 
Electrometer,  capillary,  380. 
Electromotive  force  and  concentration 
of  solutions,  365. 

measurement  of,  354. 

standards  of,  356. 

Electrons,  398. 

—  and  light  adsorption,  72. 
valency,  400. 

Elements,  i. 

—  disintegration  of,  2. 

—  periodic  classification  of,  20. 

—  potential  series  of,  386. 

—  table  of,  21. 
Emulsoids,  322. 
Enantiotropic  substances,  197. 


INDEX 


411 


Endothermic    and    exothermic    com- 
pounds, 144. 
Energy,  available,  104,  150,  332. 

—  chemical,  140,  351-354. 

—  conservation  of,  140. 

—  free,  104,  150,  352. 

—  internal,  of  gases,  46. 

—  intrinsic,  143. 

—  kinds  of,  139. 

Enzyme  action  and  adsorption,  332. 

—  reactions,  221. 

—  . —  reversibility  of,  222. 
Equilibrium,  effect  of  pressure  on,  169. 

of  temperature  on,  166-170. 

—  false,  218. 

—  in  gaseous  systems,  161-164. 

—  kinetic  nature  of,  158,  160,  241. 

—  in  electrolytes,  266-312. 

—  in  non-electrolytes,  164-166. 
Equivalents,  chemical,  8,  15,  237. 

—  electrochemical,  237. 
Ester  equilibrium,  156,  164. 
Esters,  hydrolysis  of,  206. 

—  saponification  of,  207,  275. 
Eutectic  point,  187,  191. 
Exothermic    and    endothermic    com- 
pounds, 144. 

Expansion  of  gases,  work  done  in,  27. 

FARADAY'S  laws,  237. 

Ferric  chloride,  hydrates  of,  194. 

Filtration  of  colloidal  solutions,  323. 

Fluidity,  74. 

Formation  of  compounds,  heat  of,  143. 

Freedom,  degrees  of,  179,  182. 

Freezing-point,   lowering   of,    119-121, 

194. 
Friction,  internal.     See  Viscosity. 

GAS  cells,  364. 

—  constant,  R,  26,  102. 

—  laws,  25-26. 

—  deduction  of,  31-33. 

—  deviations  from,  28,  33-35. 
Gases,  25-48. 

—  adsorption  of,  328. 

—  behaviour  of,  on  compression,  51. 

—  kinetic  theory  of,  29-35,  46. 

—  liquefaction  of,  58. 

—  solubility  of,  in  liquids,  82. 

—  specific  heat  of,  43-48. 
Gay-Lussac's  law  of  gaseous  volumes,  9. 

—  of  expansion  of  gases,  25. 
Gel  (hydrogel),  323. 
Gladstone-Dale  formula,  64. 
Grotlhus'  hypothesis,  264. 


HEMOGLOBIN,   osmotic    pressure    of, 

316. 

Heat  of  combustion,  145. 
additive  character  of,  148. 

—  of  ionisation,  285,  295,  344. 

—  of  solution,  146,  153. 
Helium,  liquefaction  of,  59. 

—  critical  constants  of,  51. 
Helmholtz  formula,  351-354,  373. 

—  views  on  valency,  399. 
Henry's  law,  82,  95,  178. 
Hess's  law,  125. 

Heterogeneous  equilibrium,  172-199. 
Hydrate  theory,  333,  339. 
Hydrated  ions,  346. 

Hydration  in  solution,  345-347. 
Hydrates,  dissociation  of,  174. 

—  —  in  solution,  340. 
Hydrogel,  323. 
Hydrogen,  adsorption  of,  329. 

—  electrode,  376,  385. 

Hydrogen    iodide,   decomposition    of, 

159,  161. 
Hydrogen-oxygen  cell,  389. 

—  peroxide,   decomposition  of,  202, 
229, 

Hydrogen  sulphide,  dissociation  of,  167. 

INDICATORS,  theory  of,  296,  309. 
Intermediate  compounds  in  catalysis, 

223. 

Ionic  and  non-ionic  reactions,  307. 
Ionisation  and  chemical  activity,  311. 

—  degree  of,  261,  281. 

—  energy  relations  in,  343. 

—  heat  of,  285,  295,  344. 

—  mechanism  of,  342  345. 

—  rdle  of  solvent  in,  314,   338,  342- 

345- 
Ionising  power  of  solvents,  338,  339. 

and  free  affinity,  339. 

Ions,  236. 

—  complex,  281,  303,  310. 

—  migration  of,  236,  243-249. 

—  reactivity  of,  306,  311. 

—  velocity  or  mobility  of,  252-254. 
Irreversible  electro-chemical  processes, 

354- 

Isoelectric  point,  320. 
Isohydric  solutions,  277. 
Isomorphism,  13  14. 
Isosmotic  solutions,  105. 
Isotonic  coefficients,  106. 

—  solutions,  105. 

JOULE-THOMSON  effect,  58. 


412        OUTLINES  OF  PHYSICAL  CHEMISTRY 


KINETIC  energy,  32,  46,  140. 

—  —  and  temperature,  32,  319. 

—  —  of  gas  molecules,  46. 

—  theory  of  gases,  29-35, 46. 
Kohlrausch's  law,  251. 

LEAD  accumulator,  397. 
Le  Chatelier's  theorem,  169. 
Light,  absorption  of,  69-73. 
Liquefaction  of  gases,  58. 
Liquids,  molecular  weight  of,  125. 

—  miscibility  of,  84,  95. 

—  properties  of,  49-79. 
Lorenz-Lorentz  formula,  64. 

MASS  action,  law  of,  155-160,  173. 

and  strong  electrolytes,  279- 

283. 

in  heterogeneous    systems, 

172. 

proof  of,  160. 

Maxima  and  minima  on  curves,  76, 

88>  339-342. 

"Maximum  work"  and  chemical  af- 
finity, 150. 
Medium,     influence    of,    on    reaction 

velocity,  224. 
Metastable  phases,  184. 
Microns,  318. 

Migration  of  the  ions,  236,  243-249. 
Miscibility  of  liquids,  84. 
Mixed  crystals,  13,  95,  190,  192. 
Molecular  attraction,  34,  58. 

—  surface  energy,  125. 

—  volume,  60,  78. 

—  volume  in  solution,  62. 

—  weight  of  colloids,  316. 

of   dissolved  substances,    109- 

125. 

of  gases,  36-43. 

of  liquids,  125-127. 

abnormal,  40,  123. 

Molecules,  velocity  of  gaseous,  33. 

Monotropic  substances,  197. 

Morse  and  Frazer's  measurements  of 

osmotic  pressure,  104. 
Movement,  Brownian,  318. 
Multiple  proportions,  law  of,  4. 

NATURAL  law,  definition  of  term,  6,  7. 
Neumann's  law,  13. 
"  Neutal  salt  action,"  84. 
Neutralization  as  ionic  reaction,  284. 

—  heat  of,  148,  283-285,  336. 
Neutrons,  400. 

Normal  electrodes,  375,  376. 


OCTAVES,  law  of,  20. 
Optical  activity,  66-69,  229- 

van't  Hoff-Le  Bel  theory  of,  67. 

Order  of  a  reaction,  213. 
Osmotic  pressure,  97-109. 

and  diffusion,  98,  108. 

and  elevation  of  boiling-point, 

109,  138. 

and  gas  pressure,  102,  103. 

and  lowering  of  freezing-point, 

109,  136. 

and  lowering  of  vapour  pres- 
sure, 109,  131. 

measurement  of,  99,  105. 

mechanism  of,  106. 

of  colloids,  316. 

Ostwald's  dilution  law,  266,  307. 
Oxidation,  definition  of,  393. 
Oxidation-reduction  cells,  390. 
Ozone-oxygen  equilibrium,  168. 

PARTIAL  pressures,  law  of,  81. 
Periodic  system,  20-24. 

—  law,  23. 

—  table,  21. 

Phase,  definition  of  term,  172. 

—  rule,  179. 

Phosphorus  pentachloride,  dissociation 

of,  163. 

Plasmolysis,  105. 
Polarization,     electrolytic,     350,     355, 


393- 

—  of  light, 
Potential  di 


66. 


differences  at  liquid  junctions, 

382. 

origin  of,  362. 

single,  376,  378-382. 

—  series  of  the  elements,  386. 
Potentials,  "  absolute,"  376,  380,  382. 
Protective  colloids,  332. 

Prout's  hypothesis,  17. 

QUADRUPLE  point,  196. 

R,  value  of,  for  gases,  27. 

for  solutes,  102. 

Radium,  2,  379. 
Raoult's  formula,  112. 
Reaction,  order  of,  213. 
Reactions,  consecutive,  216. 

—  counter,  216. 

—  side,  215. 

Reduction,  definition  of,  393. 
Refraction  formulae,  64. 
Refractivity,  63-66. 
Reversibility  in  cells,  354, 


INDEX 


Reversible  reactions,  151,  156,  222. 
Rotatory  power,  66,  229. 
magnetic,  69. 

SALT  solutions,  solubility  of  gases  in, 

84. 
Semi-permeable   membranes,   81,   97, 

105,  107,  130. 

Silicic  acid,  colloidal,  315,  323. 
Sodium  sulphate,  solubility  of,  93. 
Sol  (hydrosol),  323. 
Solubilities,    determination    of   small, 

300-302,  370. 
Solubility,  coefficient  of,  83. 

—  curves,  86,  93,  196. 

—  effect  of  temperature  on,  93,  96. 

—  of  gases  in  liquids,  82. 

—  of  liquids  in  liquids,  84. 

—  of  solids  in  liquids,  91-94. 

—  product,  298. 
Solution,  heat  of,  146,  153. 
Solutions,  boiling-point  of,  114. 

—  colloidal,  127-129. 

—  freezing-point  of,  119. 

—  isotonic,  105. 

—  solid,  94,  192. 

—  supersaturated,  92 

Solvent,   influence    of,   on    ionisation, 

338,  342-345- 
Solvents,  associating,  123,  338. 

—  dissociating,  123,  338. 
Specific  heat  of  gases,  43-47. 

solids,  11-13. 

Spectrum,  absorption,  70. 

effect  of  dilution  on,  71. 

Strong  electrolytes,  ionisation  of,  279. 

Submicrons,  318. 

Substitution,  effect  of,   on  ionisation, 

273.  276,  3°4- 

Sulphur,  equilibrium  between  phases, 
183. 

—  vapour  density  of,  41. 
Supersaturated  solutions,  92. 
Surface  tension  and  adsorption,  330. 

and     molecular      weight      of 

liquids,  125-127. 

nature  of,  129. 

Suspensions,  322. 
Suspensoids,  322. 


TELLURIUM,  atomic  weight  of,  24. 

—  position  in  periodic  table,  23. 
Temperature   coefficient    of   chemical 

reactions,  225-229. 

of  conductivity,  263. 

Theory,  definition  of  term,  7. 
Thermoneutrality,  law  of,  148,  279. 
Transition  curves,  184. 

—  points,  183,  197. 

determination  of,  198,  199. 

Transport  numbers,  246-249. 
Trimolecular  reactions,  209. 
Triple  point,  181. 
Tyndall  phenomenon,  317. 

ULTRAFILTER,  324. 
Ultramicroscope,  317. 
Unimolecular  reactions,  202,  229. 

VALENCY,  15. 

Van  der  Waals*  equation,  33-35,  53-57. 

Van't  Hoff-Raoult  formula,  112. 

—  Hoff  s  factor,  i,  125,  262. 
theory  of  solutions,  101. 

Vapour  densities,  36-41. 
at  high  temperatures,  40,  41. 

—  pressure  of  binary  mixtures,   87, 

91. 

of  solids,  173. 

lowering  of,  in. 

measurement,  113. 

Velocity  of  reaction,  200-233. 

Victor  Meyer's  method  of  determining 

vapour  densities,  37. 
Viscosity  and  electrical  conductivity, 
253,  261,  347. 

—  of  liquids,  73-77,  322. 

measurement  of,  75. 

absolute  values  of,  76. 

—  of  binary  mixtures  of  liquids,  76, 

342. 

WATER,  catalytic  action  of,  219,  220, 

233- 

—  decomposition  by,  285-293. 

—  dissociation  constant  of,  283,  293. 

—  electrolysis  of,  396. 

—  equilibrium  between  phases,  179. 

—  ionisation  of,  283,  293. 


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